For a schlenk line in chemistry where you need 0.1 - 1 mbar, sure! But this is insane physics territory... Like other people said, grease isn't behaving like you think it would at millikelvin temperatures, or at pressures lower than those in the interstellar medium.

If you have a big aluminum chamber under ultra low pressure, guess what you're concentrating in there? Hydrogen and helium from the atmosphere that's seeping through your metal. Crazy stuff that's (sadly) not fixed by slapping PTFE paste or vacuum grease onto it.