It helps to understand what employers are looking for when they advertise unlimited PTO. In many cases it's because they don't want to accumulate liability on the books for unused PTO/sick time, which they then have to pay out if you leave. They are less concerned about how much you take. (That's true for my company, certainly.)

So it's perfectly reasonable to ask for clarification about how much time off is reasonable, what are the terms for approval, etc. A decent employer will be glad to explain their policies and even put them in writing if they have not already.