I think it should be a profitable shove. Cutoff can 3b pretty wide here. You could ran that in HRC or Icmizer and check out what would be Nash. But im pretty jure AQs should just about made it in here, if there are not some bubble factors.

AQs is super awk here, I think fold is fine. Before antes unlikely an 11/11/0 (even over small sample) is getting too frisky. You're ahead of much of both ranges but if you 4bet and face a shove you're almost always way behind, but roughly priced in to call. You could 4b very small and fold to shove, but it gives villains great odds to peel in position with whole range (which is no bueno). Even when a normal size 4b gets flatted, can't assume villain doesn't have some AA-QQ and AK in their range, bad regs at these stakes love to 'trap' here. Mini pacific rim (its $16.50 BI, right?) and similar deepstack low BI tourneys we can usually find better spots to GII before getting short.

That being said I don't hate a flat either. Sure, your range is pretty face up against good hand readers, but with little history they'll at least consider that you may just be bad when you cold call in the BB. Need to call 1187 when MP is rarely 4betting but calling often, so you are usually getting around 3.8:1 on your chips. AQs flops pretty well, and many villains will play straightforward postflop fearing you might be really strong, so this can't be that bad even OOP.

Still, you are somewhat frequently dominated so A or Q high flop can mean bye bye stack more often than we'd like. I'd probably be folding with no real reads. If field is really tough you probably can 4b GII here as standard, but in low-mid BI deepstacks I don't think this is the case.