Impossible. If it's a radio-controlled watch, then it synchronises with the transmitters once every 24 hours, the rest of the time it is a standard watch.
Besides, twice a year (clocks on, clocks back) it will become wildly inaccurate as it resynchronises.
whiffy
you say its impossible but it can't be as time is whatever we want it to be it can never be wrong even if it is not showing the same time as everyone else