Hey all,
I used to be a GPS payload analyst in the 2 SOPS, the Air Force unit that operates the GPS constellation. In a nutshell, the navigation data uploaded to the satellites daily does indeed account for variance in Earth rotation.
This variance is irregular, and impossible to predict with complete accuracy, as it does arise from sources such as wind, atmospheric friction, etc. But NGA provides observation of UT-UT1 to the 2 SOPS each week. These observations are used to generate predictions of rotational variance and polar wander. These predictions are in turn used in the coordinate transformation that takes place each time a navigation upload is generated.
The tsunami did indeed have an effect on Earth rotation, but the effect was minute, and would already be absorbed into GPS predictions. If the error WAS ever big enough for us to see, it would have occurred in the time between when the tsunami occured and the satellites were uploaded with a fresh navigation message. In all likelihood, only someone heavily post-processing GPS data would notice any perturbation.
Peace,
TeamRJJO