Yes.
They call the "roll top" a tissue dispenser. I guess that's what it is supposed to be used for. However I only keep miscellaneous junk in there.
(I don't keep any gloves in the glove box either.)
By the way, when I installed this, it fit perfectly. You do have to remove the black plastic piece above the roll top. You do not have to remove the small vent piece on the dash above the instrument cluster. I also removed the right A/C, (passenger side) vent before I glued it on, but I don't think that was necessary. I also used a bunch of clamps around the roll top to help seat the dash cover firmly in this area, as well as cardboard wedged between the windshield and the new cover to help keep it in place while it set. I also jammed an old sneaker on the left side to hold down that corner while it dried. It comes with a tube of clear silicone. I asked for a color sheet to be sent to me first so I could decide which color I liked. I was very happy with the result.