It depends. At the bottom of the MIC's information scroll, there'll be something saying who that particular MIC is used by. For example, if you're playing as the Aeudi, it will say "Used by the Aedui, Arverni and Casse" (or something like that). If you share the MIC with the faction you captured the city off, there's not much point in destroying it, otherwise, yes, you should demolish it.

EDIT: Gah, too quick for me Intranetusa.