I've attempted to find evidence, and found this study, which indicates that first generation immigrants are actually very close to 4th+ in terms of welfare and taxation : https://www.cato.org/publications/economic-development-bulle...
At the same time, I found other studies showing that second generation immigrants support many left wing social policies, such as gay marriage and multiculturalism, but that recent first generation were slightly less inclined to support gay marriage.
It would seem that on the balance, naturalized immigrants (many of which are considered second generation in that study) are on the left socially but not necessarily economically.