Will alligator type wrenches mess up the head on hex-headed bolts?

No, unless you use the wrench to beat on the threads.  Don't think you will get much grip using an alligator on hex head bolts, they were made for square heads.  Is this a joke?

Sorry, meant the head, not the threads.

Same answer  ;-)

Probably will since they made a mess of plenty of old bolts back in the day.

Unless one had a specific wrench sized for a hex head and most didn't, your choice was a heavy *Monkey wrench*,  or a an alligator jaw wrench.   Actually the alligator was actually a *speed wrench*, as it could be spun and used quickly.