If I have understood the system configuration correctly, then the loss of navigation (position) input will invalidate the advanced ‘terrain’ and obstacle functions. This would be similar to switching off the advanced functions (which should not be done), leaving the old EGPWS modes (1 to 6) still functioning using the existing altimetry systems.
As described by kijangnim, with GPS embedded in EGPWS then the position function should not be lost and the enhanced functions will continue to work. However, if the GPS position information is provided externally, then the ‘terrain’ function may or may not work depending on the routing the information via the IRS/FMS, and/or the mix of other navigation sources. Most probably, they will not be working; in which case EGPWS should display the system status.
With an IRS/FMS only installation, beware of map slip as this creates an invalid position. This is not alerted by EGPWS, which will use the erroneous position when checking for terrain.