When you jailbreak a ps3, it allows you to play backups of your games you already own and run homebrew software on your ps3 console. There is nothing bad about that, but Sony realizes that ps3 jailbreaking will increase piracy, as it allows people to simply download games off the internet and copy them onto the ps3's hard drive. Sony built the PlayStation 3 if you remember, so they can detect a ps3 running a jailbreak obviously and there is no possible way to hide the jailbreak. Once you have been caught with a ps3 running a jailbreak that's connected to the PSN network, you will get banned without question. Once the ps3 console is banned its permanent and it can't be removed.
I know this because i jailbreaked my ps3 console, to play games off the hard drive, to increase the life span of the laser inside the blueray drive. I connected the console onto the internet, with the jailbreak firmware running on the console. Within second of signing into the PSN network, i was banned and can't play online.
So yes your ps3 console will get banned from playing and that is a true fact. The only way you can prevent your jailbroken ps3 from getting banned, is to play it offline and restore the original and official firmware back onto your ps3, when you want to play online using it, just to be on the safe side.