No they won't.
First off, you don't understand either Spaniard or Muslim cultures - which are related due to the Muslim occupation of Spain for 700 years (that's a long time. the effects last). In those cultures, they could care less what the standard of living is in "their territory". What is important to them is that they posess that territory. Nothing else matters to them.
Secondly, they will have no problems maintaining a standard of living above what their cultures create. The Muslims have perfected the slave society over the ages. The word "Dhimmi" and its attendant institutions - taxation on all non-believers, political isolation and deprivation of non-believers, etc ad nauseum - tells you all you need to know about the parasite society they will run. For the outsiders it will be "work for us or be exterminated".
In Mexico, and all countries left over from the Spaniard colonization, a small but vicious and relentless elite lives in lurid, gaudy wealth at a level shunned even by the hyper wealthy of this country. They do so by ruthlessly oppressing the majority of the people in their country and making sure that no one can fight back. They intend to do the same here.
Your post is merely wishful happy talk. "Don't worry, everything will turn out OK, it always does".
To put it bluntly, no it won't.
China assimilated Mongol invaders because it was a strong and ancient civilization with huge numbers, and the Mongols were eventually pulled into it.
We absolutely know, from 1,500 years of history, that that will not work with Muslims. They have conquered numerous great civilizations, and destroyed ALL of them. This includes Egypt, one of the longest lasting civilizations in the world. It includes Persia, the heir of Babylon and the middle eastern cradle of civilization. It includes India, another great and long-lived civilization which only recovered after the British moved in.
Mexican and Latin American civilization is a little more of a question. As you say, they have a brutal and selfish elite, and they have been plagued for their entire history with revolution and discontent. They have never been free for more than brief periods of time. But they are still a better bet than the Muslims. Not a good bet, however. There’s only 300 years of history there rather than 1,500, but it’s definitely not encouraging.
Your post is BS. Equating Mexicans with Muslims because some six degrees of separation parlor game is ridiculous. Equating an influx of Spanish speaking people coming here almost entirely for personal economic reasons with the designs of Muslims that want to destroy is equally silly.
Mexicans want to enjoy the fruits of our success. They're are way too many crossing the border uncontrolled. A small minority of them have leftist leanings and harbor delusions of Aztlan. Muslims want us all dead. Big difference. Relax and have a Corona.
Where does one go to sign up for the Free Republic Anti-Hispanic Paranoics club? It sure seems to have a lot of members.