Is a damper needed in the exhaust stack with a fridge converted electric smoker?

Probably wouldn't need a damper, but a cover for it would be necessary so rain or rodents couldn't get inside.

My electric fridge conversion is a bit different from traditional vintage fridge smokers. I have a 1-1/4" drainpipe in the bottom that doubles for my air intake, and a 1-1/2" smokestack coming out the top back. I have no mathmatics to back it up, but I felt the smaller outlet would make for better heat retention and put less strain on the element and PID. In that light, I opted to install a damper inside the pipe that could be opened full for smoking, or sightly closed when no smoke is being used. The wingnut is aligned with the damper, so I know what position it is in.

You may never need to use a damper, but it might be nice to have the option; and it would be a lot easier to install before you get everything put together.

Not if you can control the airflow elsewhere.