nope. the sat nav still works, and the calculations dont change. its only the theoretical understanding of why it works that changes. one hundred years ago they didnt understand the nature of particle physics as they do today, they still managed to get electricity, radio and all sorts of other technology working fine.
Fair enough - allow me to rephrase. Relativity time adjustments weren't made by trial and error - someone didn't sit there with a Sat Nav trying adjustment after adjustment until they were right. The calculations were generated directly from Einstein's theory and then, when tested, they agreed exactly.
The coincidence involved in the theory being completely wrong but the satellites' path through time being affected by the exact same amount is phenomenal. For me (and the scientists involved - hence them opening up the data and asking for others to analyse it), it's far more likely that there is an error in this experiment than in the theory.
Of course you're right in that it doesn't mean that your sat nav suddenly stops working. It does however mean we got phenomenally lucky by essentially guessing how it would work.