The plate voltage might sag a little with thirstier tubes, but it shouldn't really be a huge issue.
If you're looking to get less distortion out of Lab Rat though a more effective option would be to drop the value of the gain pot. I personally like how an A50k works in here. Cranked 100% still gets you a very good amount of drive, but you have a lot more mid-gain options in the lower spots on the dial.
The tube comes at the very end of the circuit on Lab Rat, so the tube will only distort to the extent that it's pushed by the op-amp. The majority of the distortion is still coming from the op-amp, which is why it still inherently "feels" like a Rat.