Hamachi works just like the other LMI products. It uses a SuperNode or Server to broker the initial connection and then hands off the connections to the peers, meaning that the connection is just between the client systems and nothing is going thru the server (The server does keep information on the connections and sends keep alive packets to maintain them, but you are not exchanging your data with the server).
There are exceptions to this. If Hamachi can not broker a peer to peer connection is will use a server to route your data to it's destination. In this case you data is 'flowing' thru the server, but your data is encrypted.
Your biggest issue is that technically any user that knows your network name can attempt to gain access. You can minimize this by not publishing your network and keeping a strong password.