Does upgrading a tank commander's equipment do anything?
Solution 1:
Yes
There are missions where Claude will be on foot as a Scout-class soldier, instead of in the tank (e.g. Chapter 3: Rangers in the Storm). In these missions, he'll have that equipment.
That said, you're always able to change the equipment on units while positioning them before a deployment, so feel free to not give him anything fancy, and just change that when it's relevant.