The boots would weigh you down, but you could swim - for a while, not as long or as fast or as easily as you could swim without them.
Your boots would definitely NOT fall off! They're hard to get off even when dry, sitting in a chair, with a boot jack, so when they're wet and you're flailing in the water trying to pull them off, you're not going to succeed at all.
You might drown. Depends on how well you swim, how fast and rough and deep the water is, how cold it is, and so on.