I wouldn't worry quite as much about the bottom edges of the top cabinets swelling. If you're using the spray primer, prime the cabinets in very light coats to start out with. Your first couple ought to be almost a light mist. The worst thing you can do is blast them looking for perfect coverage. Then you'll end up with drips and runs. Prime the exposed edges you're talking about along with the rest of the cabinets. They will soak up more primer because the grain is open on them. Just keep lightly applying coats of primer to all of the surfaces until you build up a solid white surface. Then you can move ahead with your actual paint. Approach that the same way. Use very light coats, let it dry, do another one, and go gradually. Eventually, everything including the exposed bottom edges should be sealed up and fine.
I didn't do any type of clear polyurethane over ours. You certainly can, but I've found so far that the white gloss acrylic enamel I used to spray is pretty hard and doesn't scuff easily. The gloss is good for sink splatter and things have wiped right off with a wet paper towel or sponge easily so far.