It will bind somewhat. But you won't see AS5 or another good paste get hard and brittle like the while ceramic based compounds. The one thing a thermal paste does is fill in the mibute gaps or pores in the cpu and sink materials with a paper layer of the compound there. You use something like a coffee filter or other non linting cloth or material when going to clean off the old grease for a new application.
Something like rubbing alcohol would be used to help break that up since it disappears once it evaporates. Other cleaning solutions would leave traces behind. That's one thing there you want to avoid since it would contaminate any fresh application. I'm just wondering how long a grease will stay good after having used only one application last spring. The tube has been sealed ever since but will it be good whenever going to use it again? That would be in years not months there.