I think Twitter is a bit faster than that. Twitter users in Japan seem to respond really fast when they feel any moderate level of shaking; at times, if you follow enough Japanese people on Twitter, your entire timeline gets filled with people saying "oh hey, something's shaking" or "it's rocking" or "boobs!". So yes, you will get advanced warning if there are people closer to the epicentre than you posting on Twitter (and as long as they are not using a certain phone provider which got overloaded during the big earthquake/tsunami last year while all the other providers were fine). And yes, this obviously doesn't work if the earthquake knocks out all the cell phone infrastructure in the areas between you and the epicentre.
Amusingly enough, I was watching a UStream broadcast run by some Japanese guy and people from a different area of Japan told him that they just had an earthquake, and he replied saying he didn't get any info here. Then, several seconds later, the earthquake alarm went off in the broadcast. So, I think Twitter isn't going to be very far off in terms of speed and definitely should be able to inform you about an ongoing earthquake as long as it's not a super short one and you're like next to the epicentre.