Has this hypothosis been tested? I don't see why an antibiotic would effect algae. Cyno is a bacteria which is why it works against it.
You don't want to use a very strong antibiotic though or use to strong a dose because this could effect your beneficial bacteria.
The kind that Woody carries is fairly safe in that regard as it is a weaker kind. (the name escapes me at the moment)
I have a refugium full of macro algae (mostly
Feather Caulerpa) that has not been effected (i have done this twice in the last year).