HT bypass with tube amp that inverts signal

I'm hoping for some advice. I want to buy a tube preamp that has HT bypass that works with the preamp off. But I have been worrying that if I get a preamp that inverts the signal and switch the cable at the speakers, then HT is out of phase if the preamp is off, right? Do I need to just look at pre amps that don't run while off instead? Hope someone out there has some experience. I'm considering either a Cary 2002 or a Conrad Johnson ET3. Any advise on either choice?