There's no guarantee. Companies may whatever intrusive monitoring they want on their computer, because it belongs to them. While running Firefox from a USB drive keeps Firefox from saving any files to the computer, it, or a plugin may still leave behind registry entries, and the network activity may also still be monitored. This is a special case for privacy, because covering your tracks on the computer doesn't really help at all when they control the entire environment - they could sniff traffic on the network, they could have a proxy server that logs traffic, they could have software that takes screenshots of the desktop, they could have key loggers, the list basically is endless. All I can really advise is to be aware of your companies IT and privacy policies, and consider the risks before you do anything on a computer that belongs to them.