I would very much suggest that you put a coat or 2 of black primer on the plastic before you put the chalkboard paint. Look at my picture. On the keezer, you can see a couple little scratches because if the white plastic underneath. The ferm chamber, I put black primer, and if there are scratches, I don't know about it cause black is what comes thru.
I have my freezers on wheels so I can roll the ferm chamber over to the boil kettle (never lift a full keg). So, they may see some bumps once in a while. Maybe not an issue for the standup fridges. With the collar attached to the lid, I have to pull them out away from the wall quite a bit to open, and sometimes, the tops hit the wall just a little (scratch....)
Anyways, just know that the chalkboard paint is really not that resilient, but it looks cool... even without chalk on it (kind of slate-y/satin finish).
FYI- Black primer is hard to find at Lowes/HD. Try Ace.