Whether approaching from the side or front course, the position will have the same magnitude of error, although with different directions.
Does the FMS update take into consideration that DMEs are slant range and not true ground distance? If so, does it measure true altitude, comparing it to the DME station elevation? The higher your level and the closer you are to the station, the greater the error. If you are 6000 feet above the DME station, the slant range error will be as much as a nautical mile when you pass over it. In this sense, a DME displaced by a few tenths of a mile should not make such a great difference?
And as you write, LEM, you are not using LNAV to fly the entire approach anyway, and even if you were, the INS also updates from the localizer, not just the DME. Since the FMC knows of available DMEs, it might even disregard displaced ILS DMEs in the first place, or know what to correct for if they are displaced?
I found this is in a Boeing 757/767 manual (
http://www.boeing.com/commercial/caf.../RNP757767.pdf page 11, updating without GPS):
The displayed ANP (ACTUAL) is computed knowing the geometry relative to the navaids for radio updating and
time since last radio update for inertial only mode. There is conservatism in the displayed ANP for radio updating in
terms of cross track position error. The sources of the conservatism are as follows:
1. ANP does not accounting for baro altitude corrections in the terminal area for the DME slant to ground
range conversions.
2. Along track latency in the navaid data due the average effect of the airplane track versus bearing to navaid.