Just to clarify, LOC provides lateral guidance only, from a ground based aid. If flying a LOC only approach, without any glideslope, using the APR mode of the autopilot will not descend the aircraft at all. You could also use NAV mode and achieve the same result.
Now the sometimes confusing part, is that many modern GPS/FMS units provide/calculate verticle guidance to non precision (no verticle guidance) approaches by creating a verticle path between waypoints, with altitudes assigned to each. This is ‘nice to have’ stuff and is not required to fly the approach (ignoring LVP approaches). Indeed, all the tolerances and weather minima are based on calculating the verticle part manually. How you fly it is up to you. AP off completely and hand flown, or on autopilot.
When using the AP and GPS/FMS derived vertical guidance, the AP modes to use actually depends on the aircraft equipment and installation. In GA aircraft, the only vertical guidance mode of most autopilots is APR, so the GPS actually creates a signal that is seen as a glideslope by the autopilot in order for this mode to work correctly, hence APR is used. On newer larger aircraft with VNAV, this function is used instead as the autopilot is capable of interpreting the verticle commands sent directly from the GPS/FMS unit.
The key is to know how it works in you specific aircraft, as everyone could be different.