is it ok to leave a tube amp on without speakers connected

Depends on certain amps.  I think my previous Cary 211fe didn't need a resistive load connected meaning you could disconnect the speakers.  But I wouldn't bother or mess with it.

Most likely the output tubes will be damaged once you remove the speaker load as the inductance in the primary is converted into a very high voltage and the power tube shorts that voltage to ground. But then again, the transformer may damage as that energy arcs across the windings since it has nowhere to go.

The answer is clearly yes you can, but not without certainly experiencing the aforementioned damage to your tube amp…but yeah…you can.

No

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.