Is there evidence of effects of votes of no confidence on enrollment?
My answer is opinion unsupported by evidence, but I think it's right. {grin}

If your student population is drawn primarily from the local area, then the publicity might dissuade a few potential students from applying.  If the student population is drawn from a wide area (nationally or international) then most potential students will never know about the vote of no confidence, no matter how it turns out.