Yes. Almost always I would recommend the all-in. Most of the time you would have a 65%-75% of tripling up with AA 3-way. Considering the fact that tournament prize structures are top heavy, the reward of going all-in (much better chance of a top finish in the MTT) is greater than the risk (getting bubbled).
Remember, a min-cash is usually only 1.5-2.2 times the buy-in which is not much more than the buy-in, but minuscule in comparison to the top 3 payouts.
That being said, in my opinion, there are very specific situations where you may want to lay AA down.
1) Satellite bubbles when you feel as though you would satellite through anyway. Here, the risk is high and the reward is minuscule since you would qualify anyway.
2) In a regular tournament, when you are
super poor. This one is in my opinion. My reason for this is that even if you win the hand, your stack would still be very small, and as such, the value of your chips would still be lower than the value of the min. cash. By
super poor, I mean your stack is lower than about half the starting stack size.
NOTE: Keep in mind, the answer to the question, like many questions, is context-dependent. It depends on things like prize pool structure, stack sizes, and how deep you are (i.e. how many big blinds you have, both in absolute terms and in relation to other people in the tournament).
BEST OF LUCK WITH THE GRIND!!!