Yes, from earth rotation the INS could figure out true north if the latitude is known. Or figure out the latitude if current heading is known. But normally it's aligned with a starting position from pilot input or GPS.

If you are at an airport you will sometimes notice large signs giving Longitude and Latitude of the individual stands at an airport. These are used to give the initial position to the INS via the FMS. Of course these are now all built into the database these days so are only used (if at all) for gross error checking.