I would think the fact that Jeff (a guy who really doesn't seem to like RPG's in general much less JRPG's) actually ended up liking Persona 4 and thinking it was okay says a lot about how good a game it is. That said. No. It doesn't have random encounters. At all.
I would probably like the game too, but it is on intellectual grounds that I object to playing the game.
Here's the way I see it, random encounters are the result of causality. But if games aren't meant be good, (and obviously they aren't or else there wouldnt be randomly triggered encounters) and instead are merely the result of causality, then why bother playing games? They are just a waste product. It creates an existentialist crisis for me as a player/consumer. Admiring Persona 3 would be like admiring a rock.