Last I checked, there were at least 14 different status groupings for those who have come into the country -- most of these still fall under the (questionable) heading of quasi-legal status, resulting from laws made by Democrats, locally and at State levels. To toss back to Mexico, those who came across illegally, but are given quasi-legal status by local or state government laws, is to open the door to tossing out legal citizens of the US, broadly speaking.
But were I to go with your economic theory in re illegals, I would hazard to say this: I've seen statistics provided over past 10 years which portray that resulting from 40+ years of racialist pandering by hucksters in the Black Communities and Liberals United In Politics, low-income blacks tend to consume and not produce -- be on welfare, etc.; consuming any profit margin of every producer (company, employee, entreprenuer, etc.). Statistics do show that most illegals come and work, and due their very nature in being illegal, will more likely shy away from welfarian systems, and while working under the table and not directly paying taxes -- they do pay taxes at local levels (gas, foods, consumables).
Some assert this benefit ratio is offset by the crimes of certain illegals. This can be true, but as it is yet difficult to get any hard numbers of most matters concerning illegals, it is difficult to assert any which way.
At very least then, one could assert the illegal criminals are increasing investments in police, INS, courts, etc. Also job-boosting, unemployment stats.
Then there is the issue of illegals and quasi-illegals sending their income back to Mexico. This then props up the Mexican economy. As the Mexican economy is propped up, yes, through the transferrence of American dollars, businesses also grow in Mexico. As businesses in Mexico grow, more people in Mexico might find more of an incentive to stay in Mexico and add to their own economy.
But, my having said all this, endless times before, only infuriates border bots and racialists.
Illegals are crashing the medical systems in several major parts of the country. Local governments give them all sorts of benefits. Around here the local, federal and state welfare people hunt them down to sign them up for benefits. I suspect that is a general condition throughout the country as I live in one of the less benefit-friendly areas. One arm of the government, INS, makes occasional desultory walkthroughs and arrests a few illegals, most of whom they release with instructions to appear on some hearing date in the future.
Mostly I'm trying to figure out at least a semi-sane reason behind the madness other than, well, they (our "leaders") don't take their constitutional obligations very seriously (to put it kindly).
I suspect it's a fools errand.