Yes , very much possible along with microbial inoculants.

Yes you can. Please have a look at these links and PDF attachments.

https://www.motherearthnews.com/organic-gardening/hydroponic-gardening-zmaz76mjztak

http://www.advancednutrients.com/articles/organic-nutrients-and-fertilizers-used-in-hydroponics/

Dr.Arvind Singh,good information especially from your second reference attached.If on uses organic sources of plant-nutrients like sea weed kelp,fishmeal,earthworm casts etc.,there should be right conditions for mineralization of organic material through appropiate aeration and stirring(except for K which can be solubilized from organic material ).As I understand ,the organic material added should not invite the infection by any harmful organisms like E.Coli,Salmonella etc.The rate of mineralization should also match with the plant nutrient demand in hydroponics.The demand  for nutrients may be more many times and continuous replenishment may be needed  for plants .Humic acids especially fulvic acid loaded /complexed/chelated with micronutrient cations can easily be used.Use of aminoacids may serve only limited purpose as you can not supply all the required aminoacids that too in right proportion needed by different plants.Though I am not an hydroponic expert,these are some of my thoughts.

Certainly,  this is a strong possibility in years to come. Each producer has to  optimize the fertilizer regime for their crops and in their production system. It is important to try out changes to the nutrient management program on a small scale before making widescale alterations, and the more that you can monitor along the way — pH and EC monitoring is a must — will help ensure that you have the knowledge in hand to make adjustments for success...by Williams et al..PDF enclosed

Organic Fertilizers for Greenhouse Tomatoes: Productivity and Substrate Microbiology by  Zhai et a l (2009, HortScience 44:800-809):  High  concentrations of both organic liquid feeds resulted in lower yields as a result of treatment-induced fusarium crown and root rot. In contrast to some previous studies, those treatments showing fusarium crown and root rot also had the highest gross microbial activity. Measures of gross microbial activity and numbers of microbivorous nematodes were higher (average of 37% and 6.7 times, respectively) in compost/organic feed treatments than in the hydroponic control. Community physiological profiles of the bacterial populations, on the other hand, did not differ between organic and hydroponic treatments. Nematode populations were significantly correlated with gross microbial activity in the organic treatments.

You have to check because soilless growing system is not permitted in organic agriculture 

Dr. Govi, yes you may use humic acid based organic fertilizers in hydrophonics but be careful to apply, only with tested critical doses required by your crops. I have one suggestion, if you really want to improve root efficiency then would be better to  spray biosynthesized nano-P, Zn or Fe on foliage with recommended doses, we find that under hydrophonics biosynthesized nanofertilizer improves root efficiency at least by 32-50% under different arid crops.

You have to check because soilless growing system is not permitted in organic agriculture. If it concerns the use of organic fertilizers in hydroponics and not an organic production system  you can neglect this check. 

regards

I suggest to use these organic fertilizers as foliar spray in recommended doses to avoid the infection of harmful organisms ,and have the best results you wish to have.

best regards

Different biofertilizers can be sprayed and mixed in water for observation of good results