I would like to point out that most commentaries argue with the Rambam’s opinion here, and in very sharp ways.
This all follows his opinion that תכלית השכר is a spiritual world and Moshiach will not live forever.
Most disagree with that approach.
See the Raavad.
The Ramban (יגזור הרב ז”ל מיתה על המשיח ועל דורו)
Avodas Hakodesh: הרמב”ם ז”ל שפט משפט מוות על בני תחיית המתים ועל המשיח ודורו
And many others.
Additionally, when Moshiach comes, all מומים and sicknesses will be healed (as ruled by the Rambam as well, הלכות תשובה פ”ט), so I doubt anyone will still be childless. (See also Shabbos 30b)
Irregardless, throughout the signs that the Rambam gives to identify someone as Melech haMoshiach (הלכות מלכים פי”א ה”ד), he makes no mention of having children.