Yemen's unrest is far more than another version of the Arab Spring's yearning for freedom (however it is understood by the protesters). Yemen has long-standing tribal and political divisions that have sparked war before. Those factors are present today.
Stratfor worries about chaos that will allow al Qaeda to thrive.
It seems that either the government wins, and until the government wins their best troops trained and equipped by our government so they can go after al Qaeda in the Arabian Peninsula will be busy defending the government.
Or the more Islamist-friendly opposition wins, and at least initially won't work with us to fight al Qaeda. They'll disband the best anti-terrorist units, too, because they are pro government. We might have a window of opportunity to use whatever data we have on al Qaeda locations in Yemen to hit them during the transition period.
And in the meantime, al Qaeda can operate more freely and expand while both sides focus on each other and leave al Qaeda alone.
I tend to think that any government will eventually want our aid to hunt jihadis since the jihadis will eventually be a threat to that government. But in the short run, al Qaeda in the Arabian Peninsula could strike us and kill Americans or other Westerners by exploiting the lack of pressure on them.