I don't really know what the actual *rate* of finding a HA *or* a Shiny here is, but I have an idea. The rate of HA's appearing apparently gets higher if the person whose Safari you're in is online at the same time as you are, which can be a problem if you don't personally know the person. I don't think the rate is low enough that HA's would be too big of a problem to find. The rate of Shinies appearing here are apparently greater than in normal gameplay, but I doubt that it's raised enough that looking for Shinies doesn't change from being extremely monotonous. I'm not too sure about Horde Encounters, but I can assure you that looking for HA's this way will be harder, as you can't really tell which one has the HA.
As a side note, when I was looking for HA Quagsire before I knew about the other person having to be online, I caught about 30 of them before I caught a Shiny, which was probably just luck (I wasn't even looking for a Shiny).
Even if all FS Pokémon have two 31-IV stats, trying to find a Shiny, let alone one with a Hidden Ability, for competitive use isn't worth it, as it probably won't have the Nature you're looking for, nor the good IVs for the right stats. If you do happen to find one with perfect stats and abilities, you should probably go buy a lottery ticket. You will also look like a hacker.
Anyways, that's all I can say. Sorry if I couldn't give you an exact number.