Your amp’s standby switch is more than just a mute for break-time between takes or services. In the past, the standby switch was added to insure that rushes of incoming current didn’t overwhelm the tubes, causing a phenomenon called cathode stripping (this is bad).
Designing with this in mind, modern amps don’t necessarily need a standby switch. But your tube amp isn’t necessarily a modern amp. So here are some general rules of thumb (disclaimer: don’t blame me if your amp explodes).
If your amp has anything in the circuit for inrush current limitation, or if it’s got a 5AR4, GZ34, EZ81, 6AX5, 6CA4, or EZ80 tube in the rectifier, you can skip the standby switch. Plugging into a power conditioner and using its master power switch does the same thing as the power switch on your amp—just cuts AC supply to the amp. So you’re good.
The reason: These tubes have an indirectly heated cathode (sounds like a personal problem). They take about as long as the other tubes in your amp to heat up. In other words, they’re warming up to operational temperatures before anything nasty appears in the circuit.
If your rectifier tube is a 5Y3 or a 5U4, you could hurt the amp by ignoring the standby switch—they operate differently from 5AR4’s. They’re heated directly. It’s also a no-go with solid state rectifiers because they will generate high voltage faster than a tube can heat up.
Long story short: Unless you’re sure, turn standby on before power and let the tubes have at least a few seconds to warm up before taking standby off and rocking.