According to the US census, roughly 3M undocumented people own a home and there are approximately 144M housing units total. So, ~2% of the market is from the undocumented. Additionally, less than half of the entire undocumented population makes more than $28k a year.

So you're right, it is totally, 100% unrelated. Otherwise you're making a claim that one of the poorest demographics in the US with the least amount of home ownership is somehow responsible for a massive price spike in housing over the last few years.