I think you are dealing in absolutes here, and those are not really helpful.
Taxes raised from imigrants will only exceed spending on immigrants if the level of immigration is not so high that more people immigrate than can find work.
The idea that the economy simply expands automatically because people immigrate is pretty lame.
No it is not Americas productivity is far higher then Mexicos due to a huge technological advantage. This means that people immigration from Mexico to the USA will produce more goods then they would of fi they had stayed in Mexico meaning immigration leads to more GDP growth
Are you in favour of letting 500 million people immigrate into the US?
**** yea because
1) We'd be able to better compete with CHina
2) It would result in 500million people going from deep poverty to semi poverty
3) it would cause total world GDP to increase by a substantial amount
So plz explain why you want to make the world poorer