I've folded A/A in a double-or-nothing tournament, which is pretty much like a satellite.
Folding in an MTT is stack specific. Let's say you're in an MTT, the blinds are 150/300 blinds, and you were knocked down to 500 stack. With 100 people left to the money, you probably need to double up to make the bubble. But if there are only 2 or so people left until the bubble, you will cash 95% of the time by folding A/A when a couple people are all-in ahead of you.
So realistically in a $10 tournament you'll win $12, 95% of the time by folding, for an
expected value of $11.76. (Really, in a really big MTT it's probably closer to 100%)
Now let's say that you shove in that latter situation. Someone UTG opens to 900 with K/Qh and gets a call by the maniac who has 5c/7c. It's folded to your button and you call with Ad/As. The blinds fold.
In this situation you're about 60:40 to win about 2,000 chips (due to antes). So you win $0 about 40% of the time, and more than triple-up 60% of the time.
The question is, is getting 2,000 chips 60% of the time (winning least $12, 60% of the time) better than folding and getting an almost guaranteed $12 payout?
By calling, you average a $7.32 payout and have 2,000 chips but folding gets you an average $11.76 and keeps you at 900 chips.
The thing is, the bubble of an MTT is not deep. The payout structure is really flat, and 2,000 chips with 150/300 blinds is has you at an M of 4.4, which still desperate.
So maybe if you win your 60%, you advance another two or three payout levels and make $14 or $15 instead of the $12. Those extra $2 or $3 aren't quite worth the risk. (60% of $15 = $9, while 98% of $12 was $11.76).
And what about those players on your left who folded in the latter situation? They had a good chance to knock you out, but folded. These are people who you may be able to steal from when you shove with your remaining $900 when the bubble breaks in (probably this hand).