It's easy two see how the GTN works because Garmin built a nice simulator, but Garmin has never built sims for its autopilots and the documentation is not always clear. So, I did a bunch of tests today, and found that the logic is actually pretty simple. For all these tests, I started in NAV mode on a GPS track to an IF just prior to the FAF on an ILS or LOC approach.
Auto Switch: With GTN Auto Switch enabled, the GTN will fly via GPS to the IF, roll steer to the final approach course, and once the active waypoint changes to the FAF, switch the CDI to VLOC. It doesn't matter whether the loaded approach is a ILS or LOC -- it works the same.
GFC ROL reversion: If GFC APR is pressed (which arms LOC and GS) before auto switch, the GFC will capture the localizer after the Auto Switch without reverting to ROL. If APR is not armed, it will revert to ROL when the CDI switches. This means that Auto Switch will only work without ROL reversion on an ILS.
Auto Switch disabled: With APR armed, the GFC will revert to ROL if the CDI is switched to VLOC far enough from the localizer course to end up with full deflection after the switch.
I leave it as an exercise for someone else to determine how far you can be offset from the localizer and have the manual CDI switch not cause a ROL reversion .
EDIT: From the documentation, I believe that it is probable that a manual CDI switch from GPS to VLOC will not cause the GFC 500 to revert to ROL if the CDI ends up being a half scale deflection or less on the localizer, but I haven't tested this. It does not revert if the CDI ends up centered.