I wouldn't risk ordering it. There are 2 things you can do.
1. Go to Guest Services in any of the parks or DTD, show them your Chase and an ID and they will give you a rewards card. Then you call a 1-800 number and they transfer the funds immediately. They have a Mickey phone at Guest Services you can use to make the call.
2. You can order the card now (as long as you have the mininum- I think $20), transfer more funds as they become available to the card just before you leave. I typically will transfer funds to a card more than once during a vacation.