No, the gift card cannot be used to purchase Disney Dollars, sorry! It is is the Standard Operating Procedures. You can, however, use your gift card to purchase park tickets, which was not allowed previously.
Gift cards may be used on Disney.com, the catalog and in The Disney Stores, but not at the parks. So, if you know someone who is going to the parks, make sure to purchase Disney Dollars instead of the Gift Cards, if you plan on giving them "Disney type" spending money for their trip.
Also note that Disney Dollars cannot be returned for cash without an original receipt.