Can I use these tree stumps for a table?
I would not let the bugs remain either, If it is cold outside where you are now as it is here in MD USA, the warm inside temps will make the bugs quite active again. I had that happen with a cherry burl I was turning, luckily I put it in a large clear plastic bag solely for the purpose of slowing moisture loss to reduce checking. After a few days I checked the bag and there were hundreds of carpenter ants crawling around inside.
The varnish, or any paint, even wax that seals the end grain will reduce the amount of rapid moisture loss, and there for reduce the amount of checking. Without the sealer, it will split more aggressively.