If the AI has any sense of urgency, e.g. has any data suggesting that it may be shut down as time passes, it will have to move fast to do all these computations before being shut down.

The rate of bitcoin creation is a constant, not something that can be rushed. Creating more computing power to mine just ensures a greater slice of the coins as they are created. This means the AI would have to resort to other (probably more dangerous) means of acquiring wealth.