Leaving out any impacts caused by the movement of land based DGPS stations,
strictly speaking continental drift would hve no impact on GPS accuracy,
just on maps! A GPS would still say that some spot on the "spheroid" of the
world was at a specific set of co-ordinates, and they would be the same
tommorrow as today. However, the land masses would have slid sideways under
those co-ordinates. So a map showing the Washington monument to be at UTM X
and Y would be wrong. But a GPS that showed UTM X and Y to now be some
distance away from the monument would be correct. While to the casual
observer it would appear that the GPS was now reporting different
co-ordinates for the monument, and therefor the GPS was wrong, in fact the
monumnet had moved away from its original co-ordinates and the GPS was
correctly reporting the movement by reporting a "wrong" or different
position for the monument. The assumption that just because we stand on the
continent, it must be immovable is a common perception problem among you
eathlings. As a complete OT topic - its fun to learn about all the ways in
which the intellectual giants of the past tried to mathematically and
scientifically justify the Earth being the center of the universe. They had
real problems with the apparent retrograde motion of the planets - kind of a
parallel to assuming GPS must be wrong because the position of the monument
changed. Same kind of perspective issue. If we start with the assumption
that the continents are fixed (we are the center of the universe), GPS must
be wrong. The moral: you can't assume a critial variable is a constant and
arrive at a reasonable analysis.
To expand the question a bit more, if we then consider WAAS or DGPS, I think
the answer becomes more complex. As a layman who only has become as
immersed an an English lit degree will allow, I believe those systems assume
that the base station computing corrections "know" their exact position on
the face of the earth and therefor can compute error from the position as
reported by the GPS system. If the exact position of the base station(s)
change over time, I would guess that some correction of the computationally
"correct" position (the DGPS position relative to its spot on the land
surface - its spot on a map) must be resurveyed as well. This would be
relative to the resolution of the technology. If we have GPS technology
that was accurate to a few meters, and few mm might not be important (or
even noticed). However, when we have GPS systems that employ the technogy
to measure the movments of mountain peaks, then a minute amount of drift
would not only be noticed, but become very significant in employing the
technogy to it maximum ability.