Morgana~ is correct when she says:

It all depends on how the user is getting out to the internet...and if the user is some how bypassing the proxy...if that is possible.
The first assumption one has to make is that if you connect to an organisation's network, that connection will be detected and that it will be logged

This leaves three basic options:

1. Use an external proxy server (anonymous public proxy, for example)
2. Use VPN (virtual pr0n network )
3. Buy a 56.6Kb dial-up modem and use a standard telephone line

In the first instance, the connection to the proxy will show up in the local logs, but what happens after that will only be in the remote server's logs.

The VPN will be logged, but probably not locally, other than the connection to it.

A telephone dial-up connection will not be logged as it is outside the network. However it is safe to assume that an organisation that logs its network activity also monitors its telephone calls, and the repeated and lengthy calls to the ISP would stand out like a sore thumb.

Those would be the basic ways that a user would attempt to avoid detailed logging by a local server.