Well, at my company, if you have any un-used vacation time then you can either take your vacation days or they have to pay you for the un-used vacation time. The only time they don't have to pay you for the un-used vacation time is if you get fired from the company.
It all depends on the situation. If you have something that you absolutely have to deal with then go ahead and take the vacation time. I don't know that they'd have a good enough reason to reject your vacation time, especially if it's for something that you HAVE to deal with right away. Plus, some people might just take a vacation before starting a new one because at a lot of jobs here, they have to work a certain amount of time before they can take a vacation. So, if you'd like to have a couple of days off before starting the new job, I don't see why you shouldn't take it. I mean, they're going to have to pay you for that vacation time one way or another anyway.......