I don't have any concrete knowledge to say Starlink satellites rely on GPS, but based on what I know about satellites with thrusters and autonomous formation flying capabilities, they almost certainly have one or more GPS receivers onboard.
My understanding is that the SpaceX ground stations uplink the orbital parameters of other satellites and/or debris and it is mostly up to the satellites to avoid a collision. You need very precise onboard location knowledge for that. Also, I bet they are using GPS time to synchronize the fleet.
Of course you can still synchronize and maneuver the satellites manually from ground stations if necessary. And they probably do that when a satellite is misbehaving. But overall the Starlink operations concept is probably tailored to mostly automated operations.
So IMO they would definitely have big issues if GPS went away suddenly.
My understanding is that the SpaceX ground stations uplink the orbital parameters of other satellites and/or debris and it is mostly up to the satellites to avoid a collision. You need very precise onboard location knowledge for that. Also, I bet they are using GPS time to synchronize the fleet.
Of course you can still synchronize and maneuver the satellites manually from ground stations if necessary. And they probably do that when a satellite is misbehaving. But overall the Starlink operations concept is probably tailored to mostly automated operations.
So IMO they would definitely have big issues if GPS went away suddenly.