I've been playing a lot of Helldivers 1 on my CFW-enabled PS3 for the past few months without issue, but I'm not aware of any other online multiplayer PS3 games that are still active. Before that, I've even went into the Playstation store and downloaded some free DLC for a couple of games that I installed on my SSD..
FYI, I did install the PSNpatch during the initial CFW installation process.
EDIT: My PSN account is over 15 years old, and I had the latest OFW already installed before I did any shenanigans to my PS3..