No need for pressure. The packing and separation process can occur even inside a tube resting on a table. It will simply take a few years instead of a few weeks or months - colloidal suspension does not last forever.
As for evaporation, silicon is the base of many greases and does not evaporate. When you pull a HSF off a CPU that got pasted with a silicon-based thermal grease after a few months, you will usually see a ring of "wet" transparent stuff around the clay-like paste patch. That's the silicon oil that got pressed out of the thermal interface over time.
The process will happen regardless of pressure but more pressure does make it happen faster.
"pump out" ? - http://www.nordsonefd.com/images/comp300.jpg