Yes you can. I have seen people growing Napier, ParaGrass in paddy fields where water is surplus. Napier enjoys more water, so I dont see any issues.
Other fodder varieties may create problems as they wont be able to survive continuous water logging.
Why are you taking this step? Dont you think paddy straw as dry fodder is also a valuable fodder resource which can be produced in your own field?
Nikhil