TFR for the United States is 1.84, while South American countries rage from 1.75 (Uruguay) to 2.26 (Bolivia)[1]. It's tricky to find data on how the US TFR breaks out demographically. It would be very interesting, to your point, to see if immigrant TFR just echos the origin country or if there's a debuff applied for living in the United States. Anecdotally, this feels true to me less more Traditional Catholic immigrant families from Mexico or El Salvador but I've no idea if the data backs it up.

[1] https://www.cia.gov/the-world-factbook/field/total-fertility...