This question is really intelligently placed. Interestingly , saline /sodic soils face an acute shortage of Fe due to oxidation of Fe-II into Fe-III . But , growing rice crop under water surplus condition has lot of advantages , soil pH  comes down considerably  ( Chemistry of waterlogged soil by Ponnamperuma, a monumental publication is worth reading in this direction  ) , thereby , hastening the ferric form of iron rapidly  converted into ferrous depending upon the extent of reduction in soil pH and leaching soluble salt s( directly related to extent of reduction in SAR and ESP) . So , growing rice crop alone brings lot of amelioration in iron availability in such problematic soils. Now the next question comes , whether or not , we need additional iron to supplemented , either  through foliar application or application of chelated iron into the soil. I think , in casre , you establish still some kind of Fe-deficiency exists in the standing crop , one foliar spray of FeSO4 will do the world of good to crop health with regard to Fe-nutrition , otherwise , i dont think , chelated form of iron application into the soil  will be so effective , since reduction soil pH or ESP is very much dependent upon the length of  the period of  waterlogging ( facilitating the leaching of reaction products of waterlogging while growing rice crop ) , and at this point of time , you no access to such chnages ...Find enclosed some PDFs for further reading...

Agreed with Dr Anoop, I add some more points for your consideration

If direct seeded rice under low land fooloded condition, then ferrous availability is there and so uptake by crop plants

If direct seeded rice under rainfed and rains are causing alternate wetting and drying type of situation then under course of aerobic/aerobic environments, the iron availability may get hampered and in that situation foliar application of ferrous sulfate may be beneficial as it directly gets available to the plants for uptake . Application of Zn as well Fe help in biofortification, ie enhancing the concentration of these elents in the grains

regards

Depending upon soil buffering capacity, reduction in salinity or sodicity will take place as a function of soil moisture regime , eventually availability of iron will depend but that possibility , we can observe only in upland direct seeded rice , while in lowland rice , possibility of supplementing an additional Fe is meagre..

Ferric deficiency is easily detected: leaf yellowing (Fe is included in the composition of chlorophyll). In case of deficiency in the soil, it is better to bring Fe as FeSO4 by foliar spraying.

One more point I wish to inform about chelates of iron as foliar application:

Three commonly used chelating agents are EDTA, DTPA, and EDDHA and they vary in their ability to provide iron over a wide range of soil pH. EDTA maintains iron in a soluble form up to a soil pH of only 6.3, DTPA is effective up to a pH of 7.5, and EDDHA maintains iron in a soluble form from pH 4.0 to 9.0. The EDDHA iron compounds is more robust in soil conditions where EDTA - iron would react with Ca with subsequent loosing of available iron.

So, EDTA-iron compounds can be  used with foliar application, while EDDHA-iron compounds are used in the soil.

One more point I wish to inform that application of Chelates of iron and manganese simultaneously in soil will show non availability of Mn, due to antagonistic effect of Fe and Mn.

crop stage of foliar application is key, and there are reports available for various crops in this regard

regards

Comprehensive reply from Dr. Anoop and Naveen, but how much role chelated fertilizers play in achieving high micronutirent utilization efficiency.

Why use EDTA-Fe when FeSO4 can be used in foliar application?

To identify possible micronutrient deficiency foliar tissue analysis is the key. Take at least 20 leaflets dry and have them analyzed. Characterize the stage of sampling by counting the leaf number of the plant and position you use should be a fully expanded leaf. Spectral analysis will give ppm of your micronutrients. As Anoop said in a flooded rice situation the condition favors iron solubility. Most micronutrient issues are in the alkaline soil situation and at low moisture levels which lead to oxidized cations which were not soluble. In rice, I believe you will more likely experience Zinc deficiency rather than iron or manganese. An Atomic spectrum of foliar samples will define any of these issues as the threshold levels for deficiencies are well-known particularly in widely grown field crops such as rice, wheat, maize etc. In terms of Iron, it is a largely immobile nutrient and it is generally not absorbed well in the inorganic iron sulfate form. The used of EDTA is called the chelated form which not only mobilizes the nutrient but also stimulates a ready absorption and translocation in the plant. Iron can be mobilized by humic and fulvic acids and if you want to use iron sulfate solubilize the material in humic and fulvic acid carrier. A short while ago my neighbor had classic iron chlorosis on her roses and I was able to resolve the issue will compost tea. A red soil is red because of iron content when alkaline high carbonate conditions occur deficiency comes from a lack of solubility not any lack of iron in the soil per se. Many of these issues are related to inappropriate soil pH which is optimized by either liming or sulfuring to get optimized solubility of the unavailable soil reserve capacity. 

Gòod response from Dr Malhotra . Yes no doubt, chelated form of Fe has better utilisation efficiency compared to non-chelated form.On the other hand cost of chelated nutrients is much higher but their doses are much lower make them economical in application. Very often their easy availability restrict their wife scale use..

Thank you so much  for  your nice answers and suggestions

We can use EDTA-Fe or FeSO4 can be used in foliar application but depends on crop and its mechanism of variety with in crop. ErdalE,et al,2004 reported that regarding leaf Fe concentration, it was seen that the effect of foliar FeSo4 on leaf Fe concentrations was higher than of Fe-EDTA in Strawberry cultivars and it published in Turk Journal Agriculture Forest,2004, 28: 421-427.

For trees the boring holes are injected under pressure with an iron chelate solution and woody species can improve rapidly within a few days or weeks. Forest trees adapted to acid soil conditions are particularly prone to iron chlorosis the hallmark susceptible tree species in North America is the pin oak. Among varieties and species, there is wide diversity in their reaction to iron chlorosis the mechanism of resisting iron chlorosis the ability to produce organic acids and chelators which promote the iron that is in soil but unavailable based on soil reaction. Iron deficiency is related to soil pHalk. The hydrangea is a good soil pH indicator showing pink flowering in areas of alkaline reaction and blue flowers in areas of acid soil reaction. The aerial flower color distribution will mirror the underground soil reaction and give an avenue of visually what is going on underground without specialized equipment needed for its monitoring.  The areas of excessive soil alkalinity can be addressed through sulfuring the area to bring the pH to near neutral. Above ph 7.3 iron chlorosis is problematic but below the same value, it is ameliorated because the problem is not the absolute absence of iron but a problem of iron mobility under the soil condition. Calcareous soils with alkaline pH and the employment of nonadapted varieties all combine together to form a perfect storm. 

Foliar application of ferrous sulphate  or soil application Fe-chelated Sunderland rice is a better choice under amended sodic soil conditions . In a crop like rice , foliar application of ferrous sulphate  or chelated iron should be deferred choice..