Yes you can connect to NAV server with the webclient and it is the whole point of introducing web client.
There is two drawbacks in the webclient.
1. User interface is different and you will have to get used to the new interface.
2. Slowness of the client. - Even in the own server, webclient response was slower than the normal client.
Addition to that webclient use internal web services of NAV and it use these web services to communicate with the server and client. As every web application, internet connection speed and the quality will directly have an impact on the quality of the service.
Therefore to have a quality and uninterrupted client you need to have a high speed and smooth internet connection.
Plus your server should meet the required requirements so that NAV can process the requests and response to webclient without a delay.
Check this posts for more info : msdn.microsoft.com/.../jj672920(v=nav.80).aspx