Good morning stiersky,
Thanks for your question and welcome to the community!
I've never heard of anyone trying to remove or alter the trim, but you can definitely paint over it with whatever color of your choice.
To do it successfully, you'll need to first use a primer that can adhere to the trim's surface. A good primer for this would not only bond to the trim, but also means you don't have to sand or scuff it to help it bond, thus saving you time.
Primers that work well for this are oil or alcohol based, such as Cover Stain by Zinsser. Once you apply it, let the primer dry for an hour.
Afterwards, you can then cover it with a high gloss top coat of paint in latex or oil based. The key is the primer. Also, be sure to use a good quality brush or roller to get smooth and professional results on the final finish.
Again, I've never heard of anyone attempting to remove the trim, since it would be integrated with the drawers, so painting over it would be the only solution to cover it....unless you just wanted the trims for another purpose.