From the MOO manual I take it the answer to this question is yes:
Space Monster: An enormous space monster invades the galaxy and
threatens to destroy your colonies. Until defeated by your star fleet, the monster
will go from system to system, destroying all of the colonies within. The space
monsters are terrific adversaries and will take quite a number of ships to defeat.
So the follow up question is this: does every engagement with it leave it w/ lasting damage?