would it be possible to put a thin layer of resin on the foam armor for strength?
While possible to put resin on the surface of the foam, I wouldn't think it's the best idea. A very thin layer would be very brittle and prone to cracking/breaking as the foam bends and flexes. Plus, you'd have to deal with the sanding and an attempt to get it smooth again.
I think that the foam is already a decent strength and one of the pluses over fiberglass is the ability to have a little flex and bend as you move around. However, there are places where you'll need extra strength, such as the helmet. In that case, I'd recommend putting the fiberglass on the inside of the foam. But instead of just laying down resin, I'd recommend lining the inside with fiberglass mat or cheese cloth and then coating that in resin. You'll get a lot more rigidity from that and be less prone to snapping and breakage. One word of caution when you're doing that, aside from the normal safety practices (respirator, eye protection, skin covering), the reaction from the resin when setting produces a lot of heat, and in the case of the foam, especially if it's held together with something like hotglue, can deform the piece while it's setting. So it's best to keep an eye on your pieces while they're setting and be prepared to work to keep them in their proper shapes while the reaction is going.