I don't see why it would hurt them at all. I have never heard of any ill effects in that regard.
We usually use good old elbow grease (removing the algae manually) & also try to look for the root of the problem.
Overfeeding is something that usually gets brought to our attention by algae! Algae starts to come back, we are overfeeding the tank! You will never completely rid yourself of it, but try to be conscious of how much & how often you feed the tank.
Also, deffinetly experiment with different photo periods. Another light option to check out would be your bulbs. When is the last time you changed them? The older a bulb is, the lower the frequency of light becomes. Algae thrives in lower light frequencies!
A phosban reactor would help if your phosphates are high, (a sign of overfeeding as well) if you don't have one, do some research, but in my opinion, do cheap fixes! There are also media bags called Chemi-Pure that are suppossed to reduce phosphate & silicates, I never really saw much of a difference in my tanks, but others have!
Feed less, change your bulbs more often, bring the tank from a 12 hour day cycle to a 8, & don't let the algae take over!!! Remove it as you see it! Good Luck!
(BTW, Although unslightly, our horses love the hair algae, they hide in it & really do enjoy having a bit around!)