Do I or do I not remove baseboards when refinishing my hardwood floor
If this were my floor, I'd remove the baseboard molding so that the floor could be refinished properly.
Of course you can leave them in place but it will be impossible to get right to the edge with the refinishing equipment and the finishing products.
What you might do is ask your supplier who does not want to remove the baseboards to provide some references where you can go and see the end result if that's possible.
I'm not at all clear what affect either way would have on the slope of the floor.