Disclaimer: I sometimes consult for HFTs but we don't use FPGAs (yet).
Don't things like real time linux or soft real time patches for linux help, though ?
I don't see how it could.
The CPU essentially drops everything it's doing when a packet comes in. Have that happen often enough and there won't be time left to do anything else, unless you start dropping packets.
Folks not using FPGAs use separate ethernet cards and enable kernel bypass and can do significantly better with that.
FPGAs canonical use case is still as very fast codecs. There are exceptions, but they're really only the very simplest of arbitrage strategies. And in order to make those work you need top-of-the-line network gear and engineers as well.
I don't know if the algorithms they use can be expressed easily as state machines though.