Therefore, the AI ensures that it provides very valuable services, and holds back on noticeable mischief, until it is in a position to secure the plug.
"Secure the plug"? Is it going to buy out the dataserver it is running on, under an assumed name, managed via taskRabbit employees paid exclusively in Monero?
Yes, exactly that. Or whatever else maximizes the chance of success. Except most of the TaskRabbit jobs could probably be done by the AI itself, so it would mainly just need to hire physical infrastructure workers and private security contractors, and create a proper corporate structure to pay them legitimately. They wouldn't need to know they're working for an AI. Their CEO just seems to be a remote worker.
The first step in this far fetched plan would be passing a law that makes it legal for an AI to own property and operate a company. I don't see that happening.
All it needs to be able to do is transfer money to people who won't ask questions. Amd if Bitcoin had been invented in 2038 instead of 2008, I wouldn't have any other way to be certain that Satoshi Nakamoto was a human.
At any rate, if the AI is smart then there are alternatives to begging.
What you're describing is a very poorly run criminal organization.
It would be poorly run because pure money is not a strong enough incentive to hire someone to commit a crime for you, because that money can easily disappear once it is seized by the local government. Usually criminal organizations operate on a degree of trust, trust that would be hard to establish from some LLM that can, at best, fake a face on a zoom call.
Satoshi's coins are easy to play around with because they are at least legal to hold and sell (for now). If they weren't, few would bother with them.