I think you can; just need to sand the surface and apply a good under coat. You may consider taking one of the doors out and show it to the local paint store (not home depot or Lowes) and get their suggestion as how to prepare it.

 

I've never had any problem belt sanding and painting over laminate. There are some specific paints available for this but I've never spent the extra money for them. It is your workshop and not a client's kitchen, if they don't get dinged up eventually then you're not using the shop enough.

 

I agree, you need to clean them with some naphtha or mineral spitits , just to be sure there is no contaminates on them . Sand them well , then give them a light coat of shellac, then paint. You can put shellac on glass and paint over it .. You will need a chisel to get it off ..