I haven't met a wallpaper that won't come off of drywall with DIF. Using plain water is NOT the recommended solution.
The key to using DIF is in following the directions TO THE 'T'. If you have a vinly or 'aluminimum-based' wallpaper, you need a Paper Tiger. drywall will get 'ruined' if you PRESS the Tiger too hard. You only need to perforate the wallpaper; NOT tear it. I've see many damaged walls from pressing too hard. Just use the Tiger and see if you've perforated the surface enough for the DIF + HOT WATER solution to get 'behind' the paper. Sometimes, you need to do a 2nd washing right before you start peeling it off. Make sure you always have a tea pot of water boiling away. And be sure to change the water and DIF per the instructions on a regular basis. It is VERY important you wait the alloted time for the DIF to do its work. If you rush the job, you won't get the desired results. Again, sometimes, you need to wash the surface again JUST BEFORE you start peeling. (I don't think this 'step' is in the instructions. I've learned it on my own.)
As for covering over the remaining paper, you may end up creating more work for yourself. Depending on the paper, it may shrink and tear once the primer/paint dries. THEN, you'll REALLY notice the 'problem'. Take your time and be sure to read the Instructions a couple of times so you're sure of what to do.
My best to ya and hope this helps.
PS: Lay some Baseboard Painter's Plastic along the bottom of the wall to 'collect' any dripping water and/or glue. You don't want this residue on your floors or carpet. WHen you're done, let the stuff on the plastic dry up and then throw it away. This way, you won't accidentally cause the residue to 'run' off the plastic.