Nobody knows :). I assume that - yes. Because GPS is under direct control of a modem, and modem is a black box doing whatever it pleases. By turning it off in the android, you just tell android not to use it. It does not really affect GPS state itself, and modem’s firmware may still access GPS data and communicate it to the cellular provider.
But this is a pessimistic speculation. To be sure, one has to audit the firmware. Since such audit is impossible - firmware is closed - I go with my speculation - expect the worst, lest you be in for a nasty surprise.
I’m not much worried about cops spying specifically on me (warranted or not), though I’ll admit I’d rather have them having to ask a judge every single time.
I am very concerned about routine data harvesting done by cellular providers and, on top of this, big tech, and their clients like banks, insurance companies and, indeed, cops. Since there is no way they would stop this practice when asked nicely - typically they will not even answer such a request - I use a phone that denies them as much data as technically possible.
My assumption is that GPS provided by the modem stays always on, and always can be queried from the cellular provider side. User can only turn off gps data communication from the modem to the applications. For example google maps can will complain about the gps being unavaialable, while at the same time the modem will happily transmit GPS data to whoever asks via cellular network.
I saw a TV news reporter take a trip around Washington DC with two Android phones turned “off”, including the cellular and wifi radios. In addition, one of the phones was put in airplane mode prior to the trip. Afterwards, the phones were turned back on in a lab that was instrumented to receive and decode the phones’ outputs. As soon as the phones were turned on and the radios were enabled, both phones did a data dump to google, which included GPS tracking of the reporter’s trip while the phones were “off”. So, although the phones were “off”, they weren’t really off. I suppose that iPhones do the same thing.
The French TV series called “Le Bureau des Légendes” https://en.wikipedia.org/wiki/The_Bureau_(TV_series) (recommended!) is fiction but rumor has it that it is quite realistic in some ways. There, the French spying agency is routinely tracking persons of interest to them via the GPS in their phones.
In the story in that series, sometimes people try to avoid this by removing the battery from their phone and then the GPS tracking continues to work for a little while, I don’t remember exactly but I think they say it’s 30 minutes or something, apparently because the GPS sits in a piece of hardware that has an internal battery that keeps it running for a while even after the main battery in the phone has been removed. When I watched that I was always wondering how realistic that part is.