The short answer to the question is "Yes, but . . . ," so you know right away that there are pros and cons to consider. Stripping wallpaper in order to make the change to painted walls is a challenge all its own. Having to deal with the residue of glue that inevitably adheres to the walls once the paper has been stripped is a major annoyance.
On the Plus Side
Painting over wallpaper adhesive can be done, and since the adhesive never remains behind in a consistent, uniform manner, texturing paint is a wise choice. However, the best advice is to prep the walls with a sealant such as Zinsser. According to Zinsser manufacturer directions: "We would suggest cleaning the surface well and applying either our Gardz High Performance Sealer, Cover Stain Primer Sealer or Bulls Eye Odorless Primer Sealer. Topcoat with the quality water or oil based paint of your choice."
In addition to using a texturing paint for the final step, another idea would be to get creative and "faux finish" the walls, starting with a base color and texturing the look by sponging, rag rolling or streaking with a slightly darker or lighter contrast color.
On the Negative Side
For the most part, painting over wallpaper adhesive is not a good idea. First, there's the water solubility factor affecting paint adhesion, followed by the crackled and uneven surface under the new paint. In all likelihood, problems such as bubbling or flaking will appear eventually, resulting in greater time, effort and expense to correct the problem. It is better to take a little more time, apply the effort to deal with adhesive removal now rather than later.
Consider a Compromise
When the desired look is solid, uniform color rather than the multi-colored pattern of wallpaper designs, it might be a good idea to consider repapering with a textured wallpaper specifically intended for being painted. Much heavier and more durable than ordinary wallpaper, this European invention can be repainted numerous times and is virtually as scrubbable as painted walls.
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