That would be a bad experience if they showed in the guide since only the primetime shows would appear and the rest would be blocks displaying "Local Programming" with the show image displaying "SIGN OFF".
For an idea of what it would look like, go to zap2it.com click the button [Change Provider or Time Zone] Select a timezone and look at channel 4 FOX
If any intrepid souls want to test using a Custom Channel m3u, here are the gracenote tvc-guide-stationid's that correspond to the schedule you see on zap2it
10212 FOX Eastern time
17084 FOX Central time
32766 FOX Mountain time
12376 FOX Pacific time
55215 FOX Alaskan time
50254 FOX Hawaiin time