I don't know about rents, but overseas investment certainly drive up price to own in Auckland NZ and Vancouver, Canada, though the latter may have stopped due to changing tax policies. Auckland is as big as SF.

If you're investing in property overseas you want the value to be stable or increasing, though. I don't think these people are value investors who would jump into a market with declining prices because the houses were suddenly underpriced -- quite the opposite, I think some would rush to get out in that case.

There is also a significant rich foreign Saudi presence in Irvine and that's definitely more of a culture clash due to the misogynistic nature of mother/son relationships. Super spoiled kids, "slavery" scandals, etc but the money "donated" to Irvine company for things like renovating the spectrum mall is massive. Considering Irvine company owns ~90% of Irvine, I think this foreign interest can't be overlooked in lieu of the more public Chinese impact.