I don't really see how this will simplify reaching staff members because even if some of them might be in the same timezone as you it doesn't mean that they're online at the same time as you.
Just check if they're online or not, and if you need a staff member who deals with some specific sort of problems (i.e. understands Brazilian), contact them instead.
Also I don't really understand how it'd be easier to get to the tournaments if you knew each Gamemaster's GMT unless you were planning to bomb them with PMs (which I'm pretty sure they wouldn't be fans of).