I have painted cabinets in mobile homes, which have similar paper / vinyl covered particle board cabinets, with success. Only problems I had were in some areas where the paper had peeled off or was really worn. In solid areas we cleaned, used a deglosser, then primed with oil base Kilz primer. Finish coat was a good quality semi gloss latex.
As stated above if the paper is missing or peeling it is more trouble. You have to sand the loose paper back to where it in firmly attached and then fill the area with water putty or something similar and sand smooth. This is labor intensive. Then prime and paint.