You can also just paint the wall with a latex paint if you are going to test the area first with a latex primer.
Why not save a step and money.
Most latex primers are not that great at covering up stains anyway.
As long as your fabric will accept the latex paint and cover well (during your test), why not just use the latex paint and go for it.
You can also use a fan to speed up the drying process of the paint so the glue under the fabric doesn't have time to get soaked.
Answer for Painting fabric on walls.
The fabric needs to be primed before painting. As for the application method, standard brush and roll should do the trick.
The main problem you could run into is the primer dissolving the glue a bit and causing bubbles. This is the same as when painting wall paper. The best primer to use is a good acrylic. This type dries fast and doesn't smell no where near as bad as the other types (shellac and oil base).
You should do a test before going out and buying some primer. Dampen a small area of fabric with water and wait for 5 minutes. Now feel with your fingers if the glue is dissolving, it will feel a little slimy. If the glue dissolves with water then I suggest using an oil based primer, something like Kilz.
Once the walls are primed and dry you can go ahead and paint.