I have been (actually am) growing fig bushes in Hydroponics. Those are Iranian mountain figs and some have reached 6-7 foot. I did it the other way round though, I grew them from seeds I got from dried fruits (yes, they did germinate fine) to plant them in soil later. The idea here was and is to have them growing quicker and stronger from start. Growing trees and bushes in soil from seeds is extremely slow and you need to provide adequate substrate, PH etc.

As for your idea, I see no problem to transplant them in hydro at that size. Except the size (big pots will be needed with lots of substrate and good support) they should do fine with the transfer to hydro (in a drip and recycle or vast system I guess). My bushes are not very demanding and quite forgiving. The only issue is that they stagnate for a long time after being transplanted to soil.

If you can grow them to full size? Well that depends on what you understand by full size and if you are able to provide enough space and support. You have to think through that- better sooner than later. Unless you prune them on a regular base - but later (in the second year) they should not be pruned in order to grow some longer branches that can set blossoms and fruits.

Is it worth it? Here also it depends on what you mean by this or what your actual goal is. Mine (I guess I have a dozen) grow fine and from that perspective it's certainly worth it. It's most probably not economical or profitable, the way you intend to do it - but I guess this wasn't your point anyway.

As for the nutrient requirements, mine did very well in high potassium (in fact my tomato formula) nutrient. Concentration is between 1.8-20 mS/cm (EC). In some other setup, they did grow fine in as little as 1.2 and if growing only fig bushes in one setup, I'd recommend a lower concentration (between 1.2 and 1.5). Last but not least: they will expand their root system according to their size and you really need to consider that fact as well.