I can't say that thought didn't cross my mind. In fact on the ceiling inside the home where the sunroom roof meets with the home's roof I had to repair some ceiling cracks that a friend of mine thought may have been related to leaking at one point. There is no active leak at this time however. Should the sunroom have a pitched roof? As of now it is just a slope with curved edges and not to mention it feels like a piece of rubber and not something that I think would be typically used like asphalt shingle or metal. So maybe if I had a pitched roof put on with gutters on all sides that might do the trick?
Unless you can get to where you have at least a 12/2 pitch I would not look at putting asphalt shingle on the roof, as that is minimum pitch according to building codes in most places. I just added a roof over a patio I extended in the back yard and at a 12/2.5 pitch I still added an ice and water barrier underneath. The solid rubberized material may be what you need if your pitch turns out to be lower. I've never installed that stuff though.