When DCUO was part of Sony trophies did not pop for free players. But now that DCUO is owned by daybreak, do the trophies pop? I heard once that Sony does not allow trophies for free to play games, but Defiance from Trion Worlds has trophies for free to play players. What is the current case for DCUO?
NO. You still have to subscribe to DCUO to be awarded trophies. You can EARN them but they will not be attached onto your profile until you subscribe.
You still cannot be awarded trophies if you are currently a "Free-To-Play" or "Premium" player. This means that you have to pay for the monthly membership in order to unlock the trophies. (You may have already earned them but you will not see them as awarded until you subscribe.) Even though DC Universe Online and SOE (now Daybreak Games Company) are separated from Sony Computer Entertainment America/Europe/Japan/etc. ("SCEX"), SCE still owns the Playstation Network and still decides which games award trophies and which games don't. (GameFAQs forum posts)
Previously with Defiance, Defiance was a "Buy-To-Play" game. Meaning in order to play Defiance, you had to buy the game once in order to play and then all the content (to an extent) was included for free. Since Trion Games decided to remove its B2P status, it got effectively "grandfathered" in to allow players to continue using trophies. (GameFAQs article)