No, a utility patent cannot be converted to a design patent via reissue.
From the MPEP 1457:
35 U.S.C. 251 requires that the “patent is, through error, deemed wholly or partly inoperative or invalid, by reason of a defective specification or drawing, or by reason of the patentee claiming more or less than he had a right to claim in the patent”; however, the utility patent is not wholly or partly inoperative or invalid. There is no error in the utility patent. It is also noted that conversion to a design patent would exempt the existing utility patent from maintenance fees, and there is no statutory basis for exempting an existing patent from maintenance fees. See also subsection IV above regarding patent term.
From the MPEP 1457:
35 U.S.C. 251 requires that the “patent is, through error, deemed wholly or partly inoperative or invalid, by reason of a defective specification or drawing, or by reason of the patentee claiming more or less than he had a right to claim in the patent”; however, the utility patent is not wholly or partly inoperative or invalid. There is no error in the utility patent. It is also noted that conversion to a design patent would exempt the existing utility patent from maintenance fees, and there is no statutory basis for exempting an existing patent from maintenance fees. See also subsection IV above regarding patent term.