I think Gordon should find out Bruce is Batman ONLY ONLY ONLY because this is Nolan's version of "the end of Batman's story".
Because we know this caps off the trilogy, the entire storyline for Nolan's vision of the dark knight, then it's fitting for Nolan to break conventional canon and have things occur like major characters dying, Gordon finding out Bruce is Bats, Batman and Selina becoming fully-fledged lovers (and not on-again, off-again), etc etc etc.
Plus, Nolan has already changed a lot of things... for example, I don't believe Lucius Fox, in the comics, knows Batman is Bruce Wayne, but in Nolan's world, he's known since the middle of Batman Begins.
Plus, there is a lot of dramatic tension to play around with if Gordon knows Bruce is Batman, because if Gordon investigates Bruce for being Batman, Gordon will know he'll have to throw the GCPD off the trail of Bruce, when he knows Bruce IS Bats.
A lot of people keep hoping the John Blake character is going to be something extraordinary, like he's gonna turn out to be Joker 2.0 or the Riddler in disguise, but I honestly think JGL isn't lying or being coy when he says he's just playing a cop named "John Blake". I think Blake is going to be CONVINCED Bruce is Batman and Gordon is going to have to keep covering up for Bruce... and by doing so he's going to realize Bruce is Batman and Blake is right.
Also, I think by making the whole world know Bruce is Batman, it will help put BRUCE on the spotlight and allow his character to grow and reach a fuller character arc by the trilogy's end. By letting the world know Bruce is Batman, Bruce will have to answer to the world for everything he's done, explain who he is, and prove it too.