EDIT: I'm more nervous now, because I've sprayed the paint and it's a pretty rough texture. I've been assuming that the polyurethane will add a layer that'll tone down the roughness. If it doesn't...that might be weird. No turning back now!
Thought I would share how this project is going. The existing countertop was nasty - burn marks and other stains from who knows what. But rather than rip out the countertop and put in a new one, I'm going to paint the formica. This makes me nervous, so I'm trying to follow all directions and do it right. I filled in holes with wood putty (why were there holes?), sanded the top, cleaned it with ammonia, and have now primed it with two coats. The longest part was taping everything off in preparation for spraying the paint on tomorrow. If you look closely you can sort of see the new sink and faucet.
I'm using a spray texture paint that's supposed to have a stone look. After a couple coats of that, I can start putting on coats of polyurethane. If all goes well, I'll have a new countertop that only cost $27.