People seem to have difficulty grasping the essential differences between an immersion suit and a dry suit. 1) An immersion suit protects from cold in the water (and air): it has built-in insulation which a (traditional) dry suit does not have. 2) After immersion, an I S does NOT keep you dry: it doesn't attempt to. It has no seals, and a certain amount of water gets in. The layer of water in the suit warms up quite quickly, and becomes part of the insulation.
So, if you want to keep dry, get a dry suit: it won't protect much from cold water and (in my view anyway) is quite uncomfortable to wear for any length of time. If you want to stave off hypothermia for a surprisingly long time (and keep snug and dry in cold weather, rather too hot in mild weather, even if you don't go overboard), get an immersion suit: you'll probably survive even though you get a bit wet. The built-in buoyancy is a bonus.
Some water will certainly get into an immersed immersion suit: it is supposed to, and you will get wet but keep warm. I suppose, in theory if air got trapped that could invert you, but in practice it tends not to happen because of the absence of ankle/wrist/neck seals.