hmm... I was faced with the same dilemna originally with a faux wood grain laminate on my Taito cabinet.
My laminate was in rough shape
as you can see here... actually it wasn't bad except for the missing chips.
Originally I was going to fill in the depressions left by the missing laminate with putty... rough up the laminate a little with sandpaper, clean, and killz/primer, and then paint. I believe it would "stick" fine giving a proper priming. I also think it would have been easier to scrape than painting on to wood.
What I ended up doing because the laminate was old, and the glue somewhat dried out, adn there was a starting point (the broken off pieces)... I went nutz with a putty knife and a hammer to work off the laminate...
That ended up working pretty good (took about 2 hours) BUT there may have been some contact cement residue left on the particle board (it's hard to tell as the cabinet has been converted so many times it could be a multitude of things) that gave a slight dimpled texture to the wood (not perfectly smooth) and seemed to have a sheen (kinda looked like/coulda been a clear coat that was only partially sanded down prior to lamination way back in the day) I took forever to sand it down... even with a hand sander... and I didn't really get all of it off...
There's a point to this rambling BTW... you might be better off with a heat gun to soften the glue, and possibly a wood safe solvent/stripper to remove any film/finish etc that may be under there IF you decide to remove the laminate.
So... with that background of my experience with removing laminate in mind... I'd say if you wanted to do it right, get the right tools (heat gun/contact cement remover putty knife/etc) and remove the existing laminate... ideally re-laminate in the one color of your choice, but you can paint if you do a good job with surface preparation.
That's just my opinion... you can probably get away with priming/painting and having it look decent, I just don't know how much of a longterm/ideal solution that'll be... know what I mean?
good luck,
rampy