The short answer is- yes. When revived and put in culture, cells may not maintain the synchronicity due to some cell death and stress-induced signaling.
Yes but Atleast give them additional 24 hour cult time because for syncronisation we give serum free media or charcoal strip which leads to cells to stress. You can store but upon thawing it will result less cell or more cell death. Synchronous culture is so that all cells will be in same stage of cell cycle. Good luck.