If it really is milk, you can store it in the fridge until you or a SO would like to drink it.
I'm pretty sure that if you DON'T pump, you'll stop producing milk. Just like when a breast feeding woman stops feeding her baby, her body gets the message that the milk is no longer being used, so it dries up becomes powdered milk. Okay, it doesn't become powdered milk, it just stops being produced until the next time it's needed or pumped for. I THINK that once the "pump" is primed, even if you let it dry up, the milk will flow a lot easier the next time.