The answer is yes IF the amp is stable. If it is not, then the amp can be damaged. If left without a load, the amp should not have a signal applied to it as without a load the transformer can arc. But I've seen many tube amps you could leave on all day with no worries - Dyna ST-70, HK Citation 2, Marantz 8b and many others.
Our amps don't care much what kind of signal is at the input. They are pretty hard to damage and we run them without a load all the time. But they don't have output transformers that can arc.
At any rate, stable design is an important feature in any amplifier; if a tube amp can be damaged without a load while at a zero input signal condition, its a pretty good bet it will be less reliable in general use. Imagine what might happen if a speaker cable accidentally is disconnected- the amp had better be able to survive that sort of thing, and most of the vintage amps from the old days can.
Our amps don't care much what kind of signal is at the input. They are pretty hard to damage and we run them without a load all the time. But they don't have output transformers that can arc.
At any rate, stable design is an important feature in any amplifier; if a tube amp can be damaged without a load while at a zero input signal condition, its a pretty good bet it will be less reliable in general use. Imagine what might happen if a speaker cable accidentally is disconnected- the amp had better be able to survive that sort of thing, and most of the vintage amps from the old days can.