At a recent conference panel, one of the topics was the role of undergraduates in faculty searches. One speaker suggested that students should only be involved if they were closely supervised by a search-committee member, including at meals and any other sessions with the candidates.
At my first institution, we generally had one or two students serving as adjunct members of a search committee, and that experience has permanently shaped my feelings on the subject. While it is certainly true that undergraduates must be carefully trained and socialized to conduct themselves properly, the advantages of involving them are great.
First, candidates will often say things to students that they would never say in the presence of other committee members. I have seen candidates both eliminate themselves from consideration by treating students with disdain, and move themselves to the top of the pool by engaging students in substantial, stimulating conversations.
Second, involving good students in the process shows candidates that an institution cares about student engagement, and (much more important) that there will be interesting students to teach should the position be forthcoming. Savvy candidates can find out a great deal about an institution through conversations with students, and while students are often criticized for various failings, they can be extremely astute readers of candidates as well, giving excellent feedback to the search committee at decision time.
On balance, involving unchaperoned undergraduates in the search process can be helpful to both candidates and committees, so long as the students are properly coached to participate.

