the ps3 will send the log file (containing all your jailbreak activity) to $ony when it is connected to the internet. in other words... if the ps3 is connected to the internet $ony will know... even though you did not sign in to PSN. this is also true even after you start the ps3 without the jb device (aka in normal mode). that's why the best way to prevent getting banned is to turn off the internet connection in ps3 altogether.
however the new gaia manager has a new features where it erased all the log/history of the ps3. but beware... this is not 100% safe from being banned.
I am closing this now, do not repost it as this has been covered in countless threads and nobody knows for sure but Sony so it's all just repeated speculation. If you wish to risk it just do it, if not then don't... the decision is your own at this point.