According to a pamphlet given out to attendees of a PlayStation demo event in Japan, a PSN release for Kingdom Hearts: Birth by Sleep is not on the cards, at least in the Land of the Rising Sun. As shown in the above picture, no PS Store icon is visible, only UMD.
To add insult to injury, a fan who attended the event twittered that a rep working there told him that there would not be a download version of the title due to licensing issues with IP holder Disney. While we cannot confirm this, it is certainly a possibility - seeing as Sony does not mandate that titles are released on PSN date and date with their retail counterpart.
Square Enix has yet to make an official comment on the matter. Whether or not this issue will prove to be a blockade for a North American or European PSN release of the title is unknown at this point.
Rumor: PSP Go users not getting Kingdom Hearts Birth by Sleep? [NeoGAF]