I've never had a problem letting them float disconected... if you want to save power you can kill the power supplies to the half of the tube not in use. (save about 2 watts / section ) this would only easily work if you have 12v supplies. (you could try the 6v heaters in series, they have the same current according to data sheets, i'd meter it first)
if you let them float (in my experience) it's fine. I dont see why this would be a problem. If you feel like grounding stuff, just make sure the heater-cathode voltages arn't exceded. this is 180 in the 12ax7. If (i dont know how) you have the cathode in one stage at a very high potential, and have adjusted the heaters to be within the range, make sure the cathode-heater-cathode volage isn't incredibly high (i'd guess twice the cathode-heater voltage or 360 volts).
ok so if you want to ground the unsed cathode go for it, unless you have some kind of crazy voltage setup.
Whats this for anyway?