No, your 14 days begins when you enter the first park, whichever you choose. But, the clock starts as soon as you visit the first park, so don't go 15 days before DC!!!! We often have DC be in the middle of our vacation and go to SW or Aquatica earlier in the week. Just take you print at home reservation to the first park and see guest services outside the gate.
Again, it is not a 14 pass ticket, but a 14 day ticket, 14 consecutive days. DC is a lot of money, and you want to make it into the park. We have traveled in Orlando for 15 consecutive days, others have stayed longer. It has happened, the only reason I double warn you.