My question is can a government stop a wallet from syncing with the blockchain if they decide to ban the currency completely and not allow anybody to use the wallet?
Will the wallet still function as normal and download the blockchain and will the user be able to send coins from the wallet to any other wallet in the world?
If they can do this then is there any way that this can be bypassed?
Please explain in detail if you could
Yes and No.
A government or your ISP can try to make it as difficult as possible to use Bitcoin by blocking your network access to Bitcoins default P2P port or by restricting / throttling your P2P traffic / bandwidth.
However, it will still be possible for a user to connect with the Bitcoin network by changing the default P2P port or by using a VPN or an anonymity network such as Tor for connectivity.
Governments and regulatory authorities have been unsuccessful in preventing the downloading of movies and music with P2P software like BitTorrent and the Bitcoin network protocol functions in much the same way.
Basically if you have working internet access, then you have access to the Bitcoin blockchain.