Yup, I would.
I would go offline while playing and just beat the campaign and practice with characters, unlock stuff etc..
But you would still have a time stamp on any trophies you got while playing offline. What if someone saw that and decided to narc?
And I know for a fact that even if you change your time/date settings, the PS3 will correct it somehow (I moved my clock ahead while offline to 3:00am to get the Insomniac Museum trophy in one of the R&C games, and when I reconnected to the internet later, the trophy was timestamped at like 2pm, even though the trophy was unlocked while the system was set at 3am)
Make a new account, play it on there.