I'm not a fan of handing out arbitrary extras. I am a fan of starting out at higher levels though. I would just say you graduate at level 4 or 5 or so. But really, I'm not a fan of the adventure academy idea, but only on the basis of personal game-world asthetics, so I have no reasonable objection to it. I suppose in a fantasy world rich in adventuring possibilities it's not so far-fetched, but it does hint at a society with a complex infrastructure, so it would stand out less in a world like Eberron, which has a more modern feel.
If you're going to include something like this I think it would be more interesting to start play while the characters are still in school. School politics can be fun, as the Harry Potter series has proven recently.
And in a world where so many people become adventurers that it is considered a viable career, so that profitable institutions rise up in support of the lifestyle, you would expect some heavy competition out there. This in itself might make an interesting campaign element, as you would expect adventuring parties to run into other adventurers bent on beating them to plunder, etc. Another logical extension of a world where a school exists to train adventurers would be the existence of companies, almost like merc temp agencies, seeking to hire graduates.
I think this kind of world also needs a solid background explanation for why adventuring is a lucrative career path. In other words, why is there so much treasure out there to plunder? Fallen empires most frequently fulfill this function. I'm off-topic here but the idea of an adventuring school itself probably deserves some attention besides just how to power up the PCs.