We don't know if the children are "qualifying" -- they could be 17 or older.  They could qualify him, though, for Head of Household status.  It might not make that much difference in tax, between MFJ and HH.  And there's no restriction on filing an amended return, MFJ, after the EIP has been collected.  

"$1,200 not worth it" is a value judgment -- it's the proposed cost of a citizenship application.  Of course a green card is needed first, and that costs even more.  We don't know if the taxpayer is paying fees to a high-dollar tax pro, or getting pro bono help from someone who wants him to stay here because he's working on a new vaccine.