Of course it could all work. Depending on the characters' ages, you have about a 15 year period where Batman could have been in business.
I feel like he was definitely with Dick for a good while. Like at least 8 of those years.
But there's time for 3 Robins in 15 years.
But that's assuming batman is around 35 or so in the present DCnU. Is that too "old" though for this younger, hipper, wave of heroes. I don't know.
It seems like Superman is definitely now younger than that. Maybe late 20's.
Who said that Bruce is the First and only Batman anyway.
It could be that Bruce himself was a Robin and then when he assumed the Bat Mantle he got Dick, Jason and Damien to replace him as Robin.
4 Robins in 5 years