No. Not even close.
MPs will enforce traffic laws and will provide SOME support for gates in a combat zone. In most places, there aren't enough MPs, so they are augmented by other Soldiers. MPs will do vehicle searches, work with local law enforcement for training, provide liasison with investigators for criminal matters, and provide guards for detainees. Most MPs will never leave the FOB to conduct a mission.
If the "base is attacked", it won't be MPs fighting. Towers are normally manned by Infantry doing additional duties. A quick response force of Infantry would be called in. Other than that, it would be whichever unit and Soldiers are near by.
When females were not allowed to be in combat roles, MP was sometimes called "female Infantry" because it was the closest they could get (MPs carry weapons). Military Police is not considered a combat arms branch.