NO. The MMSI stays with the BOAT, not the radio. From the NAVCen website:
"
MMSI Overview
Maritime Mobile Service Identities (MMSIs) are nine digit numbers used by maritime digital selective calling (DSC), automatic identification systems (AIS) and certain other equipment
to uniquely identify a ship or a coast radio station. MMSIs are regulated and managed internationally by the
International Telecommunications Union in Geneva, Switzerland, just as radio call signs are regulated. The MMSI format and use is documented in Article 19 of the ITU Radio Regulations and ITU-R
Recommendation M.585-6, available from the ITU."
It is used to identify a SHIP/BOAT NOT a radio. It gets programmed into the radio and AIS unit. Most of the time, the radio stays on the boat. The MMSI is supposed to stay with the boat for the life of it. If/when the boat is sold, the owner will need to dis-associate himself with the MMSI so the new owner can apply for it.