Good idea. I certainly would not want the bear dead. Just tranquilize it and drive it far far away.
If a bear broke into my house while I was away, I would blame myself. I wouldn’t want the bear dead. (Note: We get bear visitors every so often but the only time one ever scratched around the door, there was garbage to take to the dump in a locked bin out on the porch. Squirrels try to get in every so often; they know I’m a pushover.)
If a bear broke into the house while I was there, however, he would die. Like, really quickly.