You're intuition is very good. This is one of the main drivers of the astronomical prices of southern California real estate.
The children of native Californians have been priced out of the market, not to mention other Americans who would like to move here. You have 10 or more illegals living in a single family home, and even at low wages they have $200,000 or more to contribute to the house. And yes, illegals can and do buy houses. Good luck if this starts to occur in your neighborhood, your quality of life will take a permanent detour due to overcrowding, noise, etc.
Fortunately, we have very good code enforcement in my town in Florida. But I understand your point.