I voted no.
I have had the priviledge of training at seminars with gifted instructors who continued to teach DESPITE overwhelming physical ailments that resulted in them looking terribly "out of shape" .
Could they "keep up with what a beginner could" in terms of stamina, as one poster here suggested? Of course not. But:
could they drop anybody in the dojo with their aiki? YES
are they two of the best teachers I've ever experienced? YES
was their mere presence on the mat, with dignity and good humor despite physical disability/discomfort an inspiration? Hell YES
Maybe what we think an instructor should be is a reflection of our own values. YMMV