Can wallpaper be coated with a protective finish?
Generally, yes - you can help protect the wallpaper with polyurethane. However, once the paper is on, it's not coming off without a complete overhaul (sand it all off and redo it), and you should be aware that paper tends to fade and yellow after a while. 

Also, if you use a brush to apply water based poly then you need to apply it kind of quickly and be (kind of) gentle because wet paper is easily marred. 

Oil based urethane should be easier to use (provided the ink doesn't bleed). You should test some paper separately (perhaps test your method on a cardboard box) before applying it to the nightstand.