Not really. The precolonial southwest was fairly densely populated, with some areas exceeding their modern density. Population density grew sparser for various reasons after the mid-14th century until Spanish colonialism created some dramatic demographic changes. The southwest remained a pretty lawless place on the frontiers of empires where armed conflict was commonplace for the next few hundred years, until after the turn of the 20th century. Would you want to move into a civil war even if it had AC?

AC was coincidentally invented as all of this was clearing up, but it wouldn't become ubiquitous until decades later after the major cities had been established with large populations. And even then, I'd blame cheap accessibility of long distance transportation more than AC for the modern state.

This feels like a non sequitur?