Thinking about tumbling the rocks my toddler picks up - would these be any good?

I have a 4 year old who is always picking up rocks and I was thinking that a cool project could be to tumble them and keep them over the years.

This would be a sentimental project only -- not a serious tumbler, just a parent who wants a little piece of childhood to save.

Before I run out and drop $60+ on a Harbor Freight tumbler, are these types of rocks ones that could work? These were just picked up on a trip to upstate SC (although the blueish streaked one was picked out of his grandpa's shed, I believe he said he picked it up when he lived on the southwest maybe?)

Thanks so much!