Synchronization of a node with the block chain mainly entails downloading the block chain data and storing the necessary files to your computer's drive. And just like DaveF mentioned, there should be no problem as long as non of the data got corrupt during the process of sudden shut down. I also believe that your device processing power also has a nice role to play here.
For a majority of devices you should be able to continue from your point during the sync. I suggest that if the syncronisation hasn't gone far before the outage you could just restart the entire process to avoid a situation where you get an error after the sync is complete.