Should I actively fight as Torbjörn as far as damage output is concerned?

I find that setting up a turret near a wall and mostly repairing it while hiding from enemies is a viable (while extremely cheesy) tactic. However, should I try to support my turret with my rivet gun to get more damage or is it most efficient to keep my turret up at all times to maximize it's single-life efficiency and use my gun for defense alone? Is there a huge benefit to actively fighting as Torbjörn or should I rely on the turret?