There is no reason FPGA can't have an intensity value just like GPU do. That is all intensity is doing. Rather than work on 2^32 hashes at once it works on a smaller subset.
There's no reason why it couldn't in theory, but as far as I can tell it doesn't support one right now. Could presumably be added by a firmware upgrade in the future though.Of course theses stales would show up. They are still valid hashes just stale and a good miner (like latest version of cgminer) will submit stales if the pool advised the miner to do (which p2pool) does. So if the FPGA has too high of a stale rate the bitstream could be improved to work on a smaller subset of the nonce range.
Looks like cgminer will do actually. There are basically two choices. You can carry on working on every work unit to completion even though you get a longpoll, which is what cgminer does, or you can submit a new work unit to the single and it'll discard any results it found so far for the old work unit and start working on the new one. Either way you lose out, it's just a question of whether you lose by throwing away shares or lose by working on work units that are stale. 
