[Arran]

Rob;
It won't be full B+, it will be higher then in regular operating mode, but still less then what it would be turning the set on from a standing start, at least in sets that have a directly heated rectifier like an #80. The biggest load on the B+ is still going to be the audio amp, and that will be run all the time, those will be running at a higher B+ with the front end tubes effectively out of circuit. People will often remove and replace tubes in a radio when attempting to troubleshoot a faulty stage, or a faulty tube, and 6.3 volt tubes usually heat up fairly quickly. The only sets I have heard of where that was a complete No-No was in a three way portable, because both the tube filaments, and the B+ is coming from the same source, and you can blow out one or more of the tube filaments.
If the cathode is no longer emitting electrons, then the plate and screen grids are really just sitting there doing nothing, I found this out with the Magic Eye in a Canadian RCA set, the B+ was cut off due to a faulty tube socket, so the target was a nice bright green, but the emission of the triode was borderline to weak because the heater remained lit any time the set was on. To be fair this set had a lot of hours on it, and at least three of the six tubes in the chassis were very weak, but generally magic eye triodes have good emission, but dim targets. It's basically the same problem you get with the picture tube in an instant on TV from the early 1970s, the cathode sits there cooking at a low voltage, but unlike in that RCA radio it's doing this as long as the set is plugged in.
Regards
Arran