There’s plenty of cases where illegal aliens are using the SSN of someone else, as reported by NYT, WashPost etc.

They can and do pay taxes with ITIN instead of SSN, and some non-citizens are eligible for SSN anyway. Undocumented immigrants have paid billions in taxes annually. https://bipartisanpolicy.org/article/how-do-undocumented-imm...

The larger point that they may be omitted on reports like this may still stand, but it’s not because every single one is unable to be tabulated in the count by definition.