No, Windows does not support FileVault (so it would not boot if it was encrypted thus!) The Windows option would be BitLocker.
(perhaps it is more correct to say FileVault does not support anything but Mac OS Extended (Journaled) partitions)
If you need a great, free, cross-platform, open-source, strong encryption tool check out VeraCrypt.
Can you use FileVault on your Mac OS X partition and BitLocker on your Boot Camp Windows partition at the same time?
Theoretically it should be fine but I don't think I would do it for two reasons.
There are quite a few mentions (if you google) of the Boot Camp partition failing to boot if FileVault isn't enabled in a very specific way. That could be from early FileVault and everything might be fine now but it makes me nervous enough. If you do it clone your drive first.
It's really useful to be able to share information between operating systems. If you have both encrypted using a method the other can't handle you lose that ability. However, if you use VeraCrypt, you can host a partition file on either OS and access it from both, and mount it as required - as well as back it up, archive it etc. If you're worried about encryption strength, VeraCrypt is also the better option as you can configure it for truly paranoid security. I also like the thought that crypto experts are able to look at the source and would have blown the whistle on it by now if it claimed to be something which it was not.