Yes, in fact it should essentially be mandatory because the spatial reference system for GPS is not fixed to a point on Earth. This has become a major issue for old geospatial data sets in the US where no one remembered to record when the coordinates were collected.

To correct for these cases you need to be able to separately attribute drift vectors due to the spatial reference system, plate tectonics, and other geophysical phenomena. Without a timestamp that allows you to precisely subtract out the spatial reference system drift vector, the magnitude of the uncertainty is quite large.