Is there evidence of effects of votes of no confidence on enrollment? Is there any evidence that a successful vote of no confidence on the president of a small college will have a negative impact on enrollment?  This warning is being used by the administration of my college to encourage faculty not to vote no confidence.
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.