I would use a grout bag in grouting and then apply whatever you want to the tiles afterward to seal or enhance them.

A grout bag looks pretty much like an icing bag for decorating cakes. You squeeze a line of grout into each joint and pack it down with a dowel of appropriate diameter laid along the joint.

I'm pretty sure Home Depot and/or Lowe's sells grout bags and I know you can get them in tile stores.

A sealer is often used on stone tiles as a grout release - prevents the grout from sticking making it easier to clean up. However, on tumbled stones with the rounded edges it's pretty hard to use a grout release. If you get it into the seams the grout won't adhere well. If you don't want to fill the holes (I would fill them as they collect dirt, especially on a backsplash) just grout carefully and clean up any excess grout as you go. I have had success keeeping a spray bottle of water handy to flush out any grout that does get in the holes.

Do you grout cushioned tunbled marble?