AFAIK The moment you sent a transaction from one address to another, the whole network "knows" that the funds now belong to the new address. The wallet.dat just proves that this specific address is yours to claim the funds, there is no need for the wallet to synchronize, as long as you control your wallet file(wallet.dat) the funds are yours.
Just remember to make a new backup of your wallet.dat from time to time if you have lots of incoming transactions in your wallet, every backup wallet can "restore" up to 100 incoming transactions, so if you made a backup today and by the end of month you had more than 100 incoming transactions, your backup wallet will be able to restore only the first 100. (thats what was happening with bitcoin, I'm not 100% sure if this also aplies to PTS)