Yes, a US design application can claim the benefit of a provisional application under certain conditions.
In the United States, a provisional patent application can be filed to establish an early filing date for an invention. A provisional application can be filed for a utility patent or a design patent. If a design patent applicant has previously filed a provisional application for the same invention, the applicant may claim the benefit of the provisional application in the non-provisional design application.
To claim the benefit of a provisional application, the non-provisional design application must be filed within 12 months of the provisional application filing date. The non-provisional design application must also include a specific reference to the provisional application, such as its application number, filing date, and title. The reference must be included in an application data sheet or in the specification of the non-provisional application.
It is important to note that the non-provisional design application must claim the same invention that was disclosed in the provisional application. If the non-provisional application claims a different design, then it cannot claim the benefit of the provisional application.
The provisions governing the benefit of a provisional application for a non-provisional design application can be found in 35 U.S. Code § 172, which states:
"(a) Benefit of Earlier Filing Date.—An application for patent for a design that is filed under this chapter by any person who has, or whose legal representatives or assigns have, previously filed an application for patent for the same design, as defined in section 171, in a foreign country which affords similar privileges in the case of applications filed in the United States or to citizens of the United States, or in the United States, may have the same effect, as to such invention, as though filed in this country on the date on which the application for patent for the same invention was first filed in such foreign country or the United States, whichever is earlier, if the application in this country is filed within six months from the earliest date on which such foreign application was filed.
(b) Provisional Application.—An application for patent for a design may be filed under section 111(b) of this title in the same manner as is provided for a utility patent application. Any such application for patent for a design filed under this section shall be designated as a provisional application for design patent application and shall be subject to the conditions and requirements of this section, except as otherwise provided.
(c) Effect of Provisional Application.—A provisional application for a design patent shall be accorded a filing date and shall be designated as such. The filing of a provisional application for a design patent shall not constitute the filing of an application for purposes of section 102 of this title. A provisional application for a design patent shall not mature into a patent unless the requirements of sections 112, 131, and 151 of this title are complied with within the time period provided in section 119(e) of this title.
(d) Benefit of Provisional Application.—The right of priority provided for in section 119 of this title shall be determined in accordance with the provisions of subsections (e) and (f) of such section."
The specific requirements for claiming the benefit of a provisional application for a non-provisional design application can be found in the Code of Federal Regulations, 37 C.F.R. § 1.78.
The right of priority provided for by subsections (a) through (d) of section 119 shall be six months in the case of designs. The right of priority provided for by section 119(e) shall not apply to designs.
The provision I cited, 35 U.S. Code § 172, is the latest version of the statute governing the benefit of earlier filing dates for design patent applications as of my knowledge cutoff date of September 2021. However, it is possible that the provision may be amended or updated in the future. It is always a good practice to check for the latest version of the statute or regulation before taking any legal action or making any important decisions.