if it is a photoperiod, absolutely no worries as you can simply wait for it to heal before changin light schedule... if autoflower timing could impact yield or stress plant out during bloom and pop nanners etc.. just gotta keep eye on it, and still worth trying. tape it up, and as long as some vascular tissue is still functional, it should recover... it'll grow back stronger at the break, too.
brownish isn't a great sign... if you think it is getting mushy or infected, i'd prune it off. bsed on picture, i'd give it some time.. looks okay.
i'd use some normal tape, as the gauze portion of a bandaid might stay moins and be a foothold for microbial growth... somethign that won't trap water or absorb water etc.