That is one of the most hideous repair jobs I've seen on a TM.
That being said, based on your description, it may be mostly cosmetic. But who knows. I can't think of any common problem that would have necessitated a patch like that. The mesh type material is probably cloth used to support a patch job -- like to cover a hole. But you're not supposed to see it when you're done, and I think it's obvious the repair person here wasn't very skilled, so I doubt he used the cloth for its intended purpose. It looks like he just squirted caulk all over the place, and didn't even try to smooth it out.
The top part of the repair looks like an attempt at sealing the seal between the 2 roof panels. That's not the way to do it, of course. And having peaks and valleys in your caulking can actually CAUSE leaks, as it allows water to sit up there instead of allowing gravity to take it off the roof.
If you're getting a good deal on it and are fairly handy, it's probably something you can take care of in a weekend as you describe. That's just a guess. You won't know what's in that rats nest until you get that stuff removed and cleaned up. I don't know if the earlier model TMs (pre-2002's perhaps) had wood in that area or not. If so, rot could be a possibility, which would be challenging to fix.
Dave