It's hit and miss. The ITU database is supposed to be updated on a regular basis, but it sometimes isn't.
My MMSI number from the FCC didn't show up in the ITU database even some YEARS after it was issued. I sent an email
directly to the ITU, with a link to the FCC database showing my registration
. A couple of weeks later, my MMSI number appeared in the ITU database.
I gather from this experience, and that of others, that it's a good idea to check and see if your MMSI number appears in the ITU database and, if it doesn't, then send an email
directly to the ITU so they can add it.