Can a digital multimeter damage a powered circuit when measuring resistance?
The reason not to measure resistance on a powered circuit has more to do with possibly damaging the multimeter because of voltages that are applied from the outside. Because of the way ohmmeters work (they must pass a current through the circuit being measured, so their internal resistance can't be arbitrarily high) it's more difficult to protect them from externally applied voltage. 

If the wall sockets are wired properly there's no risk of any damage doing this, but there is an outside chance you might not get an accurate reading because there might be a small voltage present between the two grounds due to some leakage somewhere in your house electrical system. 

Why would you not just measure between the ground connection and the strap?