Can / Should I tumble these rocks?

Pic 2 and 3 are closer-ups. My son got a rock tumbler from Santa for Christmas and we are finishing up the bag of stones that came with it. I just ordered some more grit to do another batch. We found some white and clearish quarts (I think, Upstate South Carolina) hunting around, but nothing else interesting. I remembered I had a rock collection as a kid and dug it out. Can / should these be tumbled? I have no emotional attachment to them. They are on a double size piece of paper so some are fairly large, but I have a hammer if I need to downsize. Thanks in advance for any advice you can give me.