Community manager Vaeflare has just announced on the Blizzard Forums the following message:
While we think cross-platform play would be awesome, there are currently no plans to allow connectivity between PlayStation Network and Battle.net (this is pretty standard for most games that have PC and console support). As a result, the characters on your Battle.net account and PlayStation account will also remain separate. In terms of allowing an analog controller hookup for the PC, we don’t have any plans for that kind of support right now. Similarly, since Diablo III for console was designed with a controller in mind, the PlayStation version of Diablo III will not support USB mice or keyboards.
While the recent Sony press conference has revealed the PS4 as more PC-like, we must also remember that–like Vaeflare said above–Diablo 3 was announced with a few changes on the PS4 version, including direct control over their avatar’s actions.
For all of you hanging onto the edge of your seat for any word on this, perhaps, one day, we will see a full marriage between console and PC.