Yes, the temporary card without the logos should work at ATMs in China. However it will not work at merchants, which require Visa or Mastercard.

On a side note, the "Global ATM Alliance" is a bit of a scam. BofA has high charges to begin with, so even after they waive some of them at their partner ATMs, you still pay a fair amount. If you have any ATM cards from smaller banks or credit unions, take those too.