What "network sync?" When you send a transaction every node will receive it and a miner will put it in a block. If you try a doublespend, it will be refused by everyone.
Also please do not confuse blockchain with the website blockchain.info (yay, so much idiot to name a website like an important part of bitcoin, so everyone is confused...)
Well the first (and to me still primary) goal of Blockchain.info is to display the Blockchain and related statistics. So to me the name works very well. They probably should have used a different name for the wallet though.