I wouldn't mind it... I was a little confused though... you mean the 4th film Robin is introduced and taken in by Bruce and the 5th film we see the grown up version of him and he discovers Bruce's real identity and he begins to train him. And by the 6th film he's Nightwing or something that fits Nolan's films?
Not the way I would've done it, but it could work.
The way I would've done it is 4th film he's a teenager (16 or so) and his parents are killed, similar to his origin in the comics. In the 4th Bruce takes Dick under his wing and by the end of the 4th film he learns who Batman is and he begins to train him. 5 film he is Nightwing, fitting Nolan's darker film. In the 5th film they have some problems though and Nightwing abandons Batman and they make a deal. Batman guards one section of Gotham and Nightwing the other. Then in the 6th film Knightfall is made and in that film Nightwing comes to rescue Batman and they become friends again, though Nightwing tells Batman that he cannot stay. Nightwing goes to Bludhaven at the end and Batman is once again alone. Then if a 7th film is ever made (seems a little weird going past 6), then Batman will be alone with an occasional mention or even an appearance from Nightwing. Maybe at this point make a Nightwing spin-off where Batman villains seen in the Batman films (up to the point of this spinoff) such as Joker or Black Mask (maybe) are the villains in that spin-off. Maybe make a Nightwing trilogy. In that Batman makes an occasional appearance. Batman 7, 8 and 9 are made and a Nightwing 1, 2 and 3 are made. All depending on how the audience feels of more and more films being made on this... and if it becomes too much and if people are getting tired of it, or if the films start becoming like a Schumacher film then cut it off and stop it in it's tracks before it's killed. Hopefully Nolan will do do the 3rd film... and maybe he'll come back for 4, 5 and 6... and most likely a new director will have to be gotten for 7, 8, and 9... but maybe Nolan can be coaxed into making at least one Nightwing film.
Anyway to keep Nolan's Batman world alive... but keep in mind ONLY IF IT IS NOT RUINED!!! Like I said earlier... if we see a Batman Forever thing happening, stop it and don't allow it to get to Batman&Robin.. wait like a decade then come back when the time is right and continue... What I would like to see is up to 10 or even 20 films done on Batman that are a continuing series... (like Bond)... but I'd like to see each one as good as the previous! I'd like to see the 3-film curse broken... I'd like to see the... sequel-curse broken!