We've done the tour twice. I would not take a stroller, and I wouldn't take a 2 year old if it's the only child. If there's an older child in the family, then I could see doing it, but I don't think a 2 year old would be able to appreciate much of the tour. It consists of following clues on a sort of treasure map to different sections of the park. There are a few parts a 2 year old would enjoy like playing follow the leader where the leader has an assigned way to walk (such as flying), but even then, I don't think a 2 year old would be able to keep up with the other kids.
I did this last March with DD was 14 month old. Another family had a 16 month old. We were both allowed to take strollers. With the other family, mom stayed with the older son and dad pushed the stroller. The dad and I pulled up the rear a few times except when we were asked to lead the hop, skip, jump portion. I was travelling alone with DD and my then 7yo DSis. DSis and I had done the tour together before so I knew what to expect. We still had a great time and I don't feel that the stroller hindered things at all - at least not as much as carrying a 25lb 14 month old non-walker for 2+ hours.
I really don't think the stollers are a huge issue...IF you have a good CM leading the tour. When we did the tour Thanksgiving 2003, one of guests was a Grandma in one of those electric chairs accompanying her children and grandchildren. The CM we had was fantastic about making sure Grandma was included and NOT left behind...the CM even altered our route on the tour to accomodate Grandma. I thought it was great of the CM to be so aware of those with special needs.
I've done it twice, both times with a stroller in tow. It's Disney, so everywhere you go is handicapped accessible so the stroller is no problem. When you book they'll tell you they welcome strollers.
The only thing I would warn you about is when they go into a ride you'll have to park and grab your child and rush a bit to catch up. The tour guides are very accommodating, as someone else mentioned, so you shouldn't panic. The only reason I bring this up is so that you don't have too many valuables in your stroller and get caught by surprise when having to dump it.
Also, without giving anything away, I think I can tell you that at one point you may have to head into Cosmic Ray's via the stairs. Both times I just went around to the door with the ramp and met the tour inside. It actually put me in a better place to take pictures as the kiddos came into the restaurant.
It's a lot of walking, etc., so to try to do it without the stroller, IMHO, would be a nightmare.