Interesting question because the answer is not always clear in the unit's instructions manual. Some preamps (CJ Pr 16) always look like they are on standby mode when turned off. What makes it obvious it is off is that the tubes are visible from the exterior and are not lightened up. But if powered on, even on mute, the tubes are glowing.
But with a enclosed preamp like a VAC Standard, you must unscrew the top cover to check if the tubes are on under the same conditions. Furthermore, the same question arises with the tubes in the phono stage of the preamp. When is the preamp is on, do the the phono tubes light up even if the phono is not in use.
I guess the only way to make sure is to uncover the preamp while at on and see if the tubes are glowing, and switch to mute and see what's happening. In any event, if the tubes are lite up, they're wearing down.
I've installed costly NOS tubes in both my preamps. The decision is simple in my case, everything is powered off when not in use, period. In both units, have to wait a good full hour before they bloom at their best. So for serious listening, some heat up time is necessary. You can always do something else with the music in background while the preamp gets to level. But most of the time, you should still enjoy your unit right from the start with the expectancy it will be at its best an hour later.