No way! Nothing goes down any of our sink drains except dirty water. Well, you can't help but have some small food particles go down, but keeping debris out of the tanks is something I really work hard to avoid. If it gets stuck in the tank you'll wish you'd been more careful because gray tanks can smell worse than black if it's hot outside and the breeze is just right. Our friend who let pieces of chicken go down couldn't believe how foul it smelled! The odor permeated their entire motorhome and it was disgusting.
Coffee grounds should NEVER be put down ANY sink, whether home or RV. Nor should any fat of any kind. I am truly amazed how many people have never learned this lesson from their parents, as it certainly was drilled into our heads as kids.... Nor should any sanitary product be put down ANY toilet. Nothing that will not digest in your own stomach, is good for any drain. Period! Those that continue to use it otherwise, deserve all the plumbers bills they can get.