Cunego can still do it in the right circumstances. He won two mountain stages in the 2009 Vuelta; he's too threatening to be allowed to go until he's dropped a bunch of time, but he's not good enough to stick it with the best consistently.
At that Vuelta, he won a conservatively-raced climb to the Alto de Aitana (conservatively raced climb? Perfect Tour de France prep!), but his second win came from a breakaway after he came in half an hour down on Sierra Nevada.
With the stages in the first week, I wouldn't be surprised if he could find himself in a good GC position as long as Lampre don't totally drop the ball in the TTT - some stages that suit him and he can try and get close to Gilbert, plus Super-Besse could be good for him too. If he's in a good place at that point, he can always ride in the group-behind-the-front and be able to go in a late mountain breakaway to get some time back, like Horner and Plaza last year. That way I could see him getting in the top 10-15 if he's on good form. But of course, even if that goes well, you'll see the likes of Sky and Garmin riding on the front to protect 10th place if they have it, like last year.