On WP 7.1 the Socket class is missing methods like Socket.Connect(string, int) that would make this straight-forward. The available alternative Socket.ConnectAsync apparently needs a numerical IP address (passed with the SocketAsyncEventArgs object).
Moreover, methods like Dns.GetHostEntry are also missing, so you cannot easily get an IP address given a host name.
It turns out that connecting to a host with a given host name is actually quite easy. Contrary to what the questions suggests, SocketAsyncEventArgs.RemoteEndPoint can be assigned either an IPEndPoint or a DnsEndPoint object: