You'd be surprised. Think about it - even for a company like Square-Enix, bad PR travels fast. It'll start off with a nice handful of people, but it will make it into something newsworthy on a gaming news site or on Digg if there's enough noise made by the people boycotting. I'm not just talking FF, I'm talking ALL SE games. Whether you see it or not, a snowball effect will start from that, or at the very least give SE some very bad PR.
It's been done to other developers, for example, Infinity Ward. PS3 people got really pissed off at the handling of COD4 and many boycotted the DLC map packs, including me, and voiced a very loud opinion to IW about it. IW had already made their millions in COD4, but they decided to try to warm up to the PS3 crowd anyway with some stuff, and it worked for some.
The whole reason why SE is the way it is now is because people like us think voicing some outrage and boycotting won't matter to them. By saying that, we're letting them win. Well, I'm fed up with SE putting out shitty games, ruining the good old ones they used to make on top of it, and threatening to sue every time a fan project pops up. SE can go to hell and I hope they get some REALLY BAD PR out of this.