Unless there is an issue as you mention with the ILS, it shouldn't. You can put any waypoints into the flight plan, the GPS AP will simply fly them.
I see LIBP's glideslope on 22 Y starts at 2000 feet, so it should've been able to capture the localizer.
As a test, you can use the map to spawn about 15 miles out from the airport for an approach, generally in the location that will give you a straight in. Then when spawned, turn on AP on HDG and ALT mode, fly 2000, fly towards the airport, and tune the ILS frequency. Then check if it picks it up, and try to do an CDI->APR.
It's not impossible for that specific airport to have a bug with its ILS. You can always also try another airport to confirm.