Nope. He won’t shoot you when you come through a door after him. He’ll use a turn to move away. Then when you retreat he’ll pursue you back through the door most of the time. It does help if you’re pretty close when following him. He might shoot at you if he’s far enough away, but that’s part of managing the fight.
Done properly you can kill him without taking a hit.
Tom and B’Elanna, not Tom and Janeway.