Private browsing is a setting within the Browser that allows the user to 'hide' what they have been browsing from other users of the same computer.
It does this by not storing some of the data that a browser uses to keep track of what you have browsed. It maintains the information during the browsing session, but once you end the session, the information is deleted from the computer. This information includes the History, Temporary Internet files(cache)) and cookies that are used during the browsing session.
The requests that the browser makes through the proxy will not be changed based on whether the user is in private browsing mode or not. This means that the proxy will still be able to track and log all requests made by the browser and apply policy against those requests.
The only consideration when using the Private Browsing mode is that if you are using cookie-based authentication, the user may be prompted to authenticate to the proxy more often then when not using private browsing mode since the cookie that the proxy provides during the cookie-based authentication can be deleted at the end of the session instead of remaining in the browser cache.