::has a vision of a tank where the fish can't swim for the plants::
Well yeah, of course its possible, I mean, if you bought 40 fake plants and stuffed them in a ten gallon tank... But that kind of extreme situation aside, I guess it most depends on your fish and the kind of plants you use.
If you have a fish that likes a lot of swimming room, you should use less plants, but if you have very nervous fish who like to hide a lot, more plants would make them feel safer. I also agree with Joe about the edges on some fake plants. I've had some issue with the sharper ones tearing betta fins, so I try to stick to plants that are softer and have some give like real ones would.
Another concern is getting at the gravel, a nice part about fake plants is you can take them up to clean around them, but it can be a pain to do that, so consider maintenance when you set them up.
Basically, as long as you and the fish are happy, things are good. =)