If you are referring to medical school, no. Only the admissions committee can decide. LCME standard 10.2 (see last sentence):
10.2 Final Authority of Admission Committee
The final responsibility for accepting students to a medical school rests with a formally constituted admission committee. The authority and composition of the committee and the rules for its operation, including voting privileges and the definition of a quorum, are specified in bylaws or other medical school policies. Faculty members constitute the majority of voting members at all meetings. The selection of individual medical students for admission is not influenced by any political or financial factors.
If you are referring to PD's of residency programs, the answer is probably not. It is true that PD's and chairpersons have a lot more latitude than medical schools, though.