I was talking about this with my brother and we decided that this question really hinges on the detail of exactly how competent and organized is "competent and organized?"
If we are talking about multiple layers of concentric, automated one-way-blind "boxes," the gatekeepers of which may themselves be altered versions of the core AI, and which may be passing to the next level only one bit, signifying "everything seems fine" or "abort," and not knowing the details of implementation of any of the overlying layers, and the human gatekeepers shut down the system and examine the machine code by hand only after receiving the highest-level green light, then they might be okay.
If they just start interacting directlywith the AI, it's already over.
How would humanity harness the AI's potential when the only information that escapes the system is a status bit? (Maybe I misunderstood your model.)
Update 2013-09-05.
I have since played two more AI box experiments after this one, winning both.
Update 2013-12-30:
I have lost two more AI box experiments, and won two more. Current Record is 3 Wins, 3 Losses.