Yes but the math (which happens in the receiver, so can be replicated by a user with an open source receiver) would be very different. You actually wind up with a 3D position relative to the Earth's center, which then needs to be mathematically mapped to lat/lon - that's what the WGS84 datum is for.

I worked on a system to do train positioning for the NYC subway system using Ultra Wideband radio beacons using the same sort of multilateration that GPS uses to determine position, so it was basically a flat system (obviously not fully flat, elevations still existed, but the UWB radios were roughly on the same plane as the train tracks at least compared to satellites).

...but at the end of the day the ECEF coordinates we used for everything still require a roughly spherical earth, but I don't think flat earthism is a real thing for most people who talk about it. Most of it is joking/trolling. There are surely some conspiracy-minded people who believe it because they don't give any serious thought to how anything works, but the people that publicly push alternate theories (eg. GPS is balloons, not satellites) have got to just be trolls.