Since I haven't researched that in specific I don't know for sure, but I'm guessing the answer is "No." Immigrant children from developing countries typically remain relatively poor by American standards and continue to use substantially fewer resources. They don't promptly leap up to middle class American consumption levels.
We would probably be better off, environmentally speaking, to aggressively try to convince American citizens to have fewer children while having more liberal immigration policies than to aggressively try to keep immigrants out while claiming that condemning children who already exist to a life of hardship is the moral equivalent of Americans choosing to have fewer children for environmental reasons. They aren't morally equivalent anymore than "Eat the rich" is some kind of moral high ground.
We would probably be better off, environmentally speaking, to aggressively try to convince American citizens to have fewer children while having more liberal immigration policies than to aggressively try to keep immigrants out while claiming that condemning children who already exist to a life of hardship is the moral equivalent of Americans choosing to have fewer children for environmental reasons. They aren't morally equivalent anymore than "Eat the rich" is some kind of moral high ground.