I actually have to wonder if that ability is at all helpful... With normal overwatch, you shoot when the enemy is moving... I.E., probably not in cover. This just uses up your overwatch turn by firing at someone who is almost certainly in cover, plus the accuracy debuff.
I had a full non-medic support in my last playthrough (Classic). When you get the class fully leveled, it's actually quite helpful. Not usually by itself, but in combination with other abilities. Specifically Suppression and the Support ability to get two reaction shots per turn.
For example: I was fighting a terror mission. I had my Heavy suppress a Heavy Floater and put my defensive Support on Overwatch. That forced the Floater to fire instead of moving to a better spot (and getting the -30 aim penalty for being suppressed). That gave my Support a free shot on him while still letter her get off an Overwatch shot on a Chryssalid that moved up during her turn.
I think the main idea about the overwatch giving you a shot when they fire is to let you gain the advantages of having someone on overwatch (keeping the AI from moving too much) while preventing your attack from being completely wasted when they just fire at your guys in cover instead of moving. By itself it's pretty weak most of the time, and wouldn't be worth the loss of the extra movement. It only really becomes truly useful when you combine it with other stuff. Even then, I'm not sure it's actually worth it compared to the movement skill.
I did like having a fully defense geared support, though. She was a great character and pretty awesome all around. I did need to have a dedicated medic in addition, though, so I'd say it's a viable 2nd Support option.