Neogaf's Kagari surmises in a forum thread, through several sources, that PSN will be back online before the now false May 31st date:
I have had other developers confirm to me that this is the case. The internal PSN developer network is online again, at least it seems for some, although things are still a bit shaky at the moment such as lack of new account sign up.
Looks like the full network, at least the online play/account part of it, will be back soon.
Since then, he has posted various clarifications and updates:
Logic would dictate that because the developer network is coming back up, so should the regular network.
I've had several people confirm to me in private that work for several different places, and no I'm not going to give their names away out of respect for those people.
A small update: They've been doing QA on the network since earlier this week, on several games with no issues. Everything seems to be running smoothly, so full restoration is likely going to happen soon.
Without sources, this is difficult to confirm. I have tested GR's own debug PS3 and we have no access to PSN yet, so this must either be limited to a few specific developers or just a fabrication (but my gut says that it isn't).