To prime or not to prime
If I were you, I'd prime them first. Understand that paint + primer doesn't actually mean you're doing 2 coats of work. They do sell some (the top end expensive stuff) that says it works in one coat, but the dirty little secret of paint is you can generally use one coat as a primer for the next. My bet is you purchased the base grade, which has less of the primer in it than the mid and top tiers.

I would probably go with an oil-base primer here just to be safe. Wallpaper glue can sometimes cause bonding issues with your paint. All oil-base primers should help prevent that issue.