Well, to some extent, I suppose it would depend on what kind of tree it was, and how deep the screws go.
We had a mimosa tree in our backyard that was splitting down the middle. Dh ran a long threaded rod thru the tree and bolted it to help support the tree & slow the split. The tree grew around that rod. It didn't seem to harm the tree & likely extended it's life for a few years. However the tree developed a cavity that held
water & kept dropping leaves & blooms into the pool, so we cut it down to a stump. Of
course, being a mimosa, it still sends out side shoots like crazy!