When I was testing, my pet actually kept attacking, didn't think to see if it was Biting though.
It does cost you 3 globals, if you time it perfect it works out between Kill Commands. The reason I was checking was the focus generation chance through the passive I forget the name of, potentially converting another 1-2 Cobra shot to Arcane. I don't know if that proc has an ICD? I should probably check into that. I doubt its much of a gain if any, and not sure if it's possible to replicate perfect conditions on timings before BW very frequently. I only did 3 attempts at each, and I'm willing to admit even without RNG I don't do it perfectly, and don't have the time to try it hundreds of times.
Thanks for the input, Tehstool, I'll probably just keep swapping on downtime