If you're running Linux from a LiveCD on a corporate desktop, then:

1) there will be no record _on the PC itself_ of what you've done.
2) any traffic to or from the machine will be visible on the network. With the
right tools, all details of your activity will be visible.
3) any connections made to outside servers will be seen (and most likely logged)
on the firewall and traceable back to the originating PC on the corporate
network.
4) if you use an encrypted data stream (VPN), the network manager will be able
to see that encrypted stream - that will make the manager's nose twitch.
5) the corporate firewall may not let unauthorized VPN traffic out through the
firewall
6) if you're planning to go to "inappropriate" web sites, chances are that the
network admins have blocked access to those sites anyway - and they may get
alerts if people try to access those sites.
7) the corporate firewall may require an user name and password to access the
outside world.
8) if the company uses a web proxy then its entirely likely the network manager
will know exactly what you've been doing.

My recommendation? Don't screw around with Ubuntu LiveCD on the company's
assets. If you're desperate to get to specific sites, bring your personal
laptop with you, leave it in the trunk of the car, and use it at the
neighbourhood Starbucks during your coffee breaks and at lunch.

Attempting to fire your personal laptop up on the company network is likely
gonna attract attention, too.