If they are truly aquatic plants then they will (or should) thrive in your aquarium (given that they are provided with enough light). Some plants require high amounts of light while other don't need a lot of light (eg. java moss, java fern, most crypts). If they are not a truly aquatic plant, it will only be a matter of time before they start to rot and decay and turn your water quality bad. Some non-aquatic plants can live under the water for a while but eventually will die. Some LFS sell plants but not all of them are truly aquatic...make sure you check to see if yours are. I know I bought a few a while ago that were not aquatic. Your plants should be completely submerged and not be sticking out...unless of course its a huge sword plant or something like bamboo where some of the plant needs to stick out to survive.