Wallpaper should always be removed but many people don’t.
sure can just takes some xtra prep work http://www2.benjaminmoore.com/en-ca/for-your-home/painting-over-wallpaper and use longer/thicker nap rollers
Here is another excellent article on how to paint over textured wallpaper. https://www.bidvine.com/blog/painting-over-wallpaper/
Prime it first with oilbased primer. Waterbased paints and primers can loosen the glue if you don't seal it..
If it is a Textured wallpaper that is paintable - I would prime (my favorite is XIM Bonding Primer) and then paint your favorite color. Depending on the texture - a glaze would also be nice :)