The right approach to sticking a surface to a table?

PQ_Roll

Yes. It’s up to you to make the spiral as thin as possible. That one was done quickly to answer quickly to your questions. (It’s a kind of game here, answering the first, for some of us).
But if you need to be closer, take care of that, if you have a 8 edges cylinder for the inner roll, be sure to create also a 8 point curve for a 360°.

Dont worry about optimization… I’m really well informed about it since, i’ve modelised and animated my first 300 triangle character in video game industry. ;). It was really difficult for me to quit optimizing everything when coming to render. But thanks for this attention.
It should be useful for the readers.
Indeed, the subdivision was in case you want to use a displacement with dynamic paint, for cheating textile folds. Because in-fine; it was only suppositions for me, what kind of roll you needed.