Ah the story that waders pull you under is an old wives tail. Our fishing club down here (Queenstown) holds a reasonably regular event where we go to the local pools and jump in fully kitted up, and trust me no one has ever been dragged under. Simple physics really. Its essentially the same as going into the water fully clothed.
A wadding belt is a good idea, however as it does help stop the waders filling up so much when you go in, and trust me when the waders are full of water you have a hell of a time getting out of the pool with a lot of extra weight inside your waders.
I think the old wife's tail comes from people going in and panicking then getting into problems. I know that one time I knew I was going to go in making a river crossing and despite knowing it was coming, when I did go in it was quite a shock.
My advice is, that if you are going to go into a situation where you think you might end up swimming, wear a lifejacket! Best to be wearing it and not need it, rather than ending up in a situation where you wished you were wearing it.