First of all a woman is a nidda at any age if she has a discharge of blood from her uterus. It is actually not uncommon for a newborn girl to have such a discharge, and she is tamei until she goes to the mikva some 20 years later.
However today that we do not have a Beis HaMikdash and Kohanim do not eat teruma there is little practical impact in this impurity aside for the prohibition on marital relations. A Kohen today need only concern himself with impurity from contact with a dead body, and a non-Kohen need not even worry about that.
So the short answer to your question is that there may be spiritual impurity on the chair, but a man may sit on it.