No. The only way he "gave up" Robin is that he didn't try to tear the costume from the kid wearing it. Tim didn't choose to stop being Robin, he discovered there was someone else with the job.
As for the growth becoming Batman is supposed to represent for Dick... Knowing Dick, I can't view it as anything good for him. I admire the way Winick's going at it (which I think is the only viable one), but I can't see Dick perpetually and directly struggling under the memory of Bruce's Batman as a good thing. He'd stifle. Dick doesn't want to be Batman, no one sane would, and trying to sell me the concept as a graduation angers me. But Quitely's picture says it better than I do.