For all practical purposes, if you are accessing the internet from your own personal computer, then using SSL alone will prevent your network administrator from knowing the exact URL (initial DNS connection will only reveal hostname) of the images you download from https://images.google.com/.
However, if you are using your employer's computer, where the OS is installed by your system administrator, then besides turning on incognito/privacy mode to clear browsing history, there are two extra things to look out for:
- The first thing is to go through the list of trusted Certificate
Authorities (CA) stored within your browser to ensure that there is
no Man-in-the-Middle proxy root certificate installed, which can be use to
decrypt HTTPS connection if your connection passes through a MITM proxy.
- The second thing, which is more difficult to do, is to ensure that there
are no spyware or keylogger installed on your computer. These can log your site visits without you knowing it.
A simple way to overcome these two obstacles is to boot up from a Linux Live-CD to surf the web over SSL.