Paint "wall covering" (I'm talking wall paper here) in lieu of removing the wall covering could be a good thing, but then again, you might be opening up a can of worms. It depends on what type of wall covering you will be painting over. Here's what you need to know:
Paint wall covering that is paper-based is not generally recommended. This type of wall covering has a tendency to lift & bubble once your paint "hits the wall". The moisture in the paint is like putting water on your wall covering & you know what happens when you leave water saturated on your paper-based wall coverings don't you? So you may have a problem here, depending on how long it takes for your paint to dry.
"I don't know if my wall covering is made out of paper. How do I check this?"
Look at see if you have any remnants of your wall covering. If you don't, check & see if your wall covering, on the wall, is lifted in a corner or seam. Look at the wall covering closely. If the wall covering is really thin & looks like paper, & has a whitish/yellowish back, it's probably paper.
"OK, I've checked the wall covering & I think it's paper but I really don't want to spend the time it takes to remove the wall covering before I paint the wall, plus I might damage the actual sheetrock wall from the removal of the wall covering. Can't I just paint the wall covering?"
I feel your pain here. You can always make the attempt to paint your wall covering but just paint a little wall section first, to see if the wall covering stays "tight" to the wall (check this after your paint is dry). Look at your wall covering that you want to paint over. Check & see if the wall covering looks nice & tight to the wall & seams are looking good before you decide that you want to paint your wall covering since whatever you see now (flaws in wall covering,open seams,tears,lifted corners) will be magnified once your wall has been painted.
"The wall covering I want to paint over looks like vinyl & not paper. Will I have a problem painting over my wall covering?"
You should not have a problem to paint wall covering, if you know it's vinyl, as the paint will not soak through the wall covering to the back like paper wall covering. Try a "test" spot though, so you'll know what the vinyl wall covering will look like once it's painted. If your vinyl wall covering has a raised pattern or design, please realize that some of these little nooks & crannies will fill up with paint, so when the paint is dry, you may see that the wall finish looks different in some spots more so than in other areas, so keep that in mind.
When painting vinyl wall covering, do the usual "look see" to make sure the seams are tight together & perimeter edges are down. Identify any "problem areas" & make minor repairs prior to applying your paint.
Click here to enjoy some "free" video painting tips....oh yeah!
Good luck with your project!