On one hand, it makes sense to. On the other hand, I will be flooding the home page with older questions.
As long as it passes the usual threshholds of validity and salience for tagging, I think you should tag it, even if it is old.
Being pushed to the top is a feature, not a bug. (0therwise you would have tagged it as such!) It shows which questions have had the most recent activity for the scrutiny/review of everyone else. Retagging, for example, could go unnoticed and unchecked if not pushed to the top, just like more substantial in-question edits.