You could guess after 2 days. I also wrote some code which is related to this. It uses GPS to measure and calibrate millis() and the Arduino clock within hours, no need to wait 100 days. So long as you keep it inside where the temperature is 60-80 degrees it is easy to obtain accuracy of 1ppm, which is about 1 seconds every 11 days. Or even 10ppm with some effort which is 1 second every 100 days, or 3 seconds per year. The only hardware you need for this code is GPS. I also have code which uses Wifly to do the same thing with NIST server.
If you've got the time, I can help you keep it!