In the most recent update to the ATC Manual, v20.2.2, this section regarding GPS approaches was reworded.
6.9.2 — When a pilot requests the GPS Approach, Controllers must check that the aircraft has a published procedure (i.e. denoted by a prefix in their flight plan – see 6.8.9 above) that provides lateral navigation to the intended arrival runway. Controllers can then expect aircraft to continue on their Flight Plan, and at an appropriate point (such as base), clear the aircraft for the GPS Approach. Vectors, altitude assignments, and/or intercepts should not be required and the pilot is expected to follow their flight plan to the runway threshold.
There was discussion brought up about whether or not the pilot had to have an in-app GPS approach procedure added to their flight plan or if they simply needed the waypoints for a GPS procedure included in their flight plan in order to be able to be cleared for a GPS approach.
This new updated wording clarifies that question people had. If you have any questions about anything in the manual, feel free to message us.
References: 6.9.2 of the ATC Manual