Depends on how hard your water is to start with. If your water is already moderately soft you should see some results.
If it is really hard the peat won't do anything. Trust me. I've tried. All you end up with is water so black you can't see the fish.
With that said, even if the peat doesn't affect the hardness it still is beneficial to the fish. There is something that the peat adds which the fish really like as they color up, become more lively and oft times start to exhibit breeding behaviour.
I guess what I'm saying is give it a try, it can't hurt.