There have been times when I've been really hungry way before my ADR and walked up to see if we could get in. It's worked for us, but I know that's not always the case. I specifically remember being an hour early at Les Chefs de France and they seated us immediately.
I have read here that if you tried this at Be Our Guest though, they would ask you to come back no sooner than 15 minutes before your ADR.
As far as arriving late, Disney knows things happen and they will do their best to accommodate you. I've never heard of anyone being completely turned away, but you may have to wait a while if they're very busy - figured you for a no show - and put another party at your table....