You should be able to. Those "points" reside on a perfectly valid CHASE VISA gift card. If someone takes VISA? That's a VISA gift card.
Now - as my wife and I used to use that very same CHASE-Disney Card? I would be a BAD person if I did not mention the following....
1) WDW HOTELS will NOT let you "dump" your gift card dollars at check in. Like every OTHER gift card? You must have an account balance before you use it. WDW did this for a good reason - they have no WAY to refund an over payment on a Gift Card. Not even the one branded with their name.
2) CHASE-Disney Card offers 1% cash back - and MAJOR hoops. Switch to a CHASE "Freedom Unlimited" Card? NO HOOPS. And you get 1.5% cash back. No stupid "Gift Card".... no hoops. No fees.
Your family will do as you see fit.... WE dumped that silly hoop-ridden CHASE-Disney Card a good 2 years ago.... and could not be happier with the choice .