Can a design application claim priority to a U.S. provisional application?

For most practical purposes, the answer is no - a design application cannot claim priority to a U.S. provisional utility application.

Note that there is a tiny exception to this rule which applies when a U.S. provisional application is subsequently converted into a U.S. non-provisional application.  However, the practice of converting a U.S. provisional application into a U.S. non-provisional application is largely avoided because it cuts off up to a year of time from your patent term.