I've never heard this, although it may have something to do with the idea that the signal from the sourdce is sent to the tape deck and the resto f the preamp circuitry at the same time. It may be that the tape deck will draw a different amount of power from the input signal when on and off. I have noticed this recently with my Wadia directly driving a pair of full range amplifiers and a Behringer DEQ equalizer connected to a set of powered subwoofers. If I play the system with the equalizer turned off, the main speakers sound dull. When I turn the EQ on, the main speakers brighten up and get louder, even thoughthe eq is not in line with the main speakers. For this reason, I am looking for a pre-amp with buffered outputs, which are electrically isolated from each other. I suspect the same thing could happen with a tape deck, depending on the design of the preamp and the tape deck.
The other sources would not be a problem, because they are switched on one at at ime by the selector knob, so that even though they are cabled up, they are not electrically connected to the system.
Bottom line, play some music through a source with the tape deck off, then switch the tape deck on, see if the sound changes. Keep the volume low in case there is a loud turn-on thump when you switch the tape deck on.
The other sources would not be a problem, because they are switched on one at at ime by the selector knob, so that even though they are cabled up, they are not electrically connected to the system.
Bottom line, play some music through a source with the tape deck off, then switch the tape deck on, see if the sound changes. Keep the volume low in case there is a loud turn-on thump when you switch the tape deck on.