Running a tube amp without a load can cause damage.
Amp damage under those circumstances is a risk, but it is not a certainty. A brief disconnect at medium or lower volume is less likely to cause a problem than an extended open circuit with the amp cranked.
Susceptibility to damage is also dependant on the brand, model and condition of the amp.
If you've reconnected the wire and the amp now seems to play fine, I wouldn't worry about it.
I've had the speaker wires come loose and never had a problem. I also am biwired using two sets of cables and I have had one cable come loose that was connected to the bass woofer. I just reconnected it and it was fine. In fact, this is weird, but last week, I was playing my set and only one speaker was connected, as the cleaning lady accidentally knocked off the speaker wire connections to my right speaker. I was listening to music out of the one speaker for about 30 seconds before I realized one speaker wasn't on. I reconnected without a problem. I think it takes a lot more to damage a tube amp than a loose connection for a minute or so, at least in my experience. BTW, I have a conrad-johnson tube amp.
Yes.The output transformers could arc inside,more so with a signal present.Sometimes an output transformer will arc in different parts of the windings causing different results.It may sound normal,but the primary impedance may be different.It may be putting a different load on the output tubes,running warmer in one or both channels,different sound characteristic's etc.It may be fine if no arcing occurred.