Hard to say if that is not true, or just bad PR from a marketing standpoint to say that your lens coatings are so fragile.
First time I have heard that. I must say I trust my breath a lot more than any chemicals which lens makers always advise against. But maybe I am wrong.
OK, Ken Rockwell says he breathes on his lenses before cleaning them. So, that answers it.
Breathing on a lens will not affect the coating.
However, a lot of (mostly older) lenses can develop fungus-problems by doing that.
All water-containing fluids have that risk, and your breath even has virtualy no anti-fungus ingrediants.
But the 200 F2 is relatively well protected, so it is pretty safe.