I just tried this and it definitely knows your general location. I asked it for the "best fried chicken near me" and it used my city. Gaslit me as well when I told it it had access to my location and its response that it used Google and Google provided a "default search location".

Obviously it can figure out location by IP, but the lying is insulting and creepy. The fact that lying would likely work for non-technical people is even worse.