It will damage tube amplifiers.
Worse yet is "moving over" speaker wires to the amp while its powered up. A good way to damage, possibly permanently, the output stage of the amp.These statements are false.
What is true is that some amps are stable without a load and others are not.
Our (tube) amps are unconditionally stable regardless of load or input signal condition.
Most vintage tube amps are fine without a load. This is not always the case with modern tube amps. Just check with the manufacturer.