Nope, LA is too much part of the macro economy to make such an impact. Wood and labor doesn't have to come from LA and even if that would double (it won't) there would be a round zero impact on inflation in LA. The land to be build was going to be sold anyways, you just get one bidder more, or several bidders less if the council makes requirements like x% social housing.

Please, forget anything you are worrying about here, it does not apply.