It will be slack as there is no tension in that tensioner, it's bolted straight through the gear hanger.
It's a magic gear in effect, you could just get rid of that tensioner and the set up would be the same, either way it's going to run slack when the chain stretches.
Looking at the drop outs I cant tell if they are vertical or semi-horizontal, if they are semi-horizontal you could get away with fixing it.