Many many (probably 13 years now) years ago, I tried re-gluing the headliner material in my 560SEC. It didn't come out very well. You have to be VERY VERY careful with the thickness and consistency of the glue, and it ended up re-sagging in a year or two.
Generally speaking, I've not seen this work well for anyone. There may be exceptions, but I've yet to see one, at least for a DIY job.
GSXR is correct, for the "refirb" process, new material is used. For my 560SEC, I used a material that was essentially identical to the stock material.
For my E500, I looked very hard at using alcantara and also at some other materials. I ended up going with a slightly softer material in the same color shade (essentially what is often used on MBs in recent years) and have been very very happy with that. I know a lot of folks like to go the alcantara route. I just didn't feel like it was in keeping with the vehicle, and so I went with a more "normal" type of material, but in the stock color range.
I had both vehicles re-done within a few weeks of one another, by the same shop in Houston (West Side Upholstery), which is one of the better interior shops in the Houston area, and one that has some experience with MBs. This was probably 5+ years ago now.
The good thing with "refirb" is that you CAN specify new material and/or a color change. I've yet to have ANY problems with my headliners since I had them done.
Cheers,
Gerry