You can try if you want to. But tomatoes so easily root even in medium without IBA or such. Thus if you want them to have hairy roots, prick them with the Agro and insert into a tube with medium in order to SEE what happens. In soil you dont see...

you can inoculate germinating seeds and grow plants in sand or perlit.

but why?

You can try to lower the phosphorus content of the soil you are using. According to a study, low phosphorus level can effectively slow down the tap root elongation whilst promoting production of additional root hairs. This is a nutritional mechanism of the plant to scour the topsoil for more phosphorus. 

Thanks everyone for ur support. @S.Wenkart, tomato seeds are taking a long time to germinate in MS medium. Germination is relatively faster in soil and there is no contamination problem. I am in need of producing hairy roots within a period of 2 weeks. I don't germinated seedlings to start the process of agrobacterium infection. Hence, I am trying to do the process in soil rather than invitro. 

I dont germinate tomato on MS but on Nitsch.

Then they have to be kept in nearly dark for one week and then they grow very well. Under light.

Interessant idea from Jayson woth the taproot and all and the connection to phosphorus.