I just gave away a 9 horse Snapper RER and I had no issues getting up the slopes while mowing.
However, thick grass gave it issues all of the time. The single blade and relatively low speed it spins at made it hard to get a clean cut in my opinion. When the grass wasn't very tall and thick that was always a fun mower to ride at full speed though.
I would plan on having to slow down a good bit mowing thick grass.
I don't know about the bagger, but I suspect that it would work fine as Snapper has put baggers on just about every RER they ever made.