The GPS clock does operate but if the signal loss is at power up it may just indicate the last shut down time, that is it needs the satellite to update the clock as well. I have noticed this on some GPS units, they will start counting from the previous shut down time until satellites aquired.
The watch issue will depend on the category of operation. If its a charter or RPT than a clock fitted to the aircraft is required, whether the pilot caries one does not matter. However if the clock in the aircraft does fail then it would be up to the MEL whether or not you could use the GPS clock etc...