(I am not a big fan of counterfactual thinking, but in this particular case it does help to generate new insights.)
So let's assume that the protests in Tunisia had eventually gone the way of the Green Revolution in Iran: the government stayed in power, regrouped, and began a massive crackdown on its opponents.
As we know from the post-protest crackdown in Iran, the Internet has proved a very rich source of incriminating details about activists; the police scrutinized Facebook groups, tweets, and even email groups very closely. Furthermore, the Iran government may have also analyzed Internet traffic and phone communications related to the opposition.
Now, Tunisia is no in Iran. Its long-ruling dictator is now gone and the new government is unlikely to engage in repressions on the same scale. Yet if Ben Ali's regime didn't fall, it appears certain to that the authorities would be brutally going after anyone who has ever posted a damning Facebook post or an angry email. As we have seen in the few weeks leading to Ali's exit, the Tunisian cyber-police have proved to be far more skilled in Internet repression than their counterparts abroad: it's safe to assume they would have dug as much evidence as the Iranians.
This brings me to a somewhat depressing conclusion: if the dictator doesn't fall in the end, the benefits of social mobilization afforded by the Internet are probably outweighed by its costs (i.e. the ease of tracking down dissidents - let alone organizers of the protests).
The question then is whether the social mobilization afforded by the Internet provides a force that is so powerful that no dictator would be able to withstand it. Judging by the events in Iran, the answer seems to be "no"...
It's certainly good news that the revolution in Tunisia has happened - for whatever political and social reasons - just like it's good news that the Internet has played some role in it. But we shouldn't forget that if one of the enabling political and social conditions is missing, the ease of Internet mobilization may also prove to be the opposition's Achilles' heel.
P.S. Yes, I know that crackdowns used to follow failed revolutions before the Internet as well. My point is simply that technology - not just the Internet but also mobile phones - make it easier to trace protesters and dissidents. It would be very hard, for example, to trace the names of everyone who gathered on Minsk's central square to oppose the results of the recent elections in Belarus before mobile phones became ubiquitous...