BOAC's gut feeling is correct, it does but there is a caveat (as always).
If you enter the "new" level into the FMC without executing it, it shows the Time and Fuel situation as though you were already at the new level. If you insert the appropriate step (2000, ICAO etc.) the FMC then "assumes" that you will step to the new level when it recommends to do so, and considers the incremental Climb and Descent factors for the new level.
Regards,
Old Smokey