Chrisstie,
I haven't seen or heard anything about results on a tank with an anemone. I would bet that it's safe, since it's safe on other invertebrates. Worst case scenario is that the anemone becomes stressed out. I'd be surprised if it was a problem, though.
Also, as a quick update... My cheato is completely gone now. I guess after 4-5 doses, the algaecide was enough to kill it off. I've began manually pulling a lot of hair off of rocks, and did a 20 gallon water change today. That amounts to about a 15% change. Hopefully between using my on RODI unit, this algaecide, running a phosphate reactor, feeding less, and keeping a better eye on my skimmer... (and I'm about to start vodka dosing) I hope to get this nastiness behind me.
I still haven't noticed any negative effects on my livestock. My snails have been dying, but I imagine that is simply due to a lack of soft algae to eat.