But it's not like all those people would stay in their home countries and just siphon away all our sweet sweet ubi hoard. These people would become US citizens

But it's not like all those people would stay in their home countries and just siphon away all our sweet sweet ubi hoard. These people would become US citizens and their societal output would become part of the country's aggregate output, some of which presumably funds the UBI program. As long as we don't assume people from economically disadvantaged regions are inherently incapable of providing as much value as individuals in advantaged regions then the only way allowing immigration is unsustainable is if UBI itself is unsustainable.