The biggest problem is that wallpaper is made from different material which won't accept paint that well. Vinyl wallpaper, for example, won't absorbe anything (which is why it's a popular product for bathrooms and high-humidity rooms.) Paper-based wallpaper, on the other hand, will absorbe ALL types of moisture. But when you paint it, and it dries, it will shrink and may separate from the wall. Then, you have a different problem.
I suggest you remove the wallpaper and wash off the residual glue. It's not hard work; just time-consuming (to a degree.) You'll be much more pleased with the results. If you have to, have a pro do it. Then, go to your local PAINT RETAILER and ask them how you Prime and Paint a wall that just had wallpaper removed from it. Also, search the Forum using your Browser's FIND / SEARCH feature using the keywork wallpaper and press Search. Keep reading and Searching the posts that talk about how to remove wallpaper and glue from the walls. I, personally, have addressed this many times. If you don't find anything, let me know via e-mail and I'll hook you up. (I just want to get away from repeating myself too many times.)