I doubt it. It's too hard to win the Crown anymore. There's too many variables.
The Derby attracts 20 horses every year nowadays... it used to be that people were so tenative to face the best horse in the country that they'd skip the Derby leaving it with a 5-10 horse field... much more manageable. Nowadays, people don't care if their horse has a legitimate chance to win... they enter just to have the experience of entering and running in the Derby. With the 20 horse field we end up with some wild things happening in the Derby... the best horse gets stuck in traffic or forced 6 wide or something like that. Add that together with the fact that there's 2 other major GI races 2 and 5 weeks after the Derby that the horse also has to win, and that's just an awful lot to ask of a horse.
As for Big Brown, he's very inexperienced and if he gets a bad trip he might not react well to it (remember the way War Pass stopped when he didn't get his way in the Tampa Bay Derby?)... he doesn't look like much of a closer (he had the stamina to keep his pace all the way to the finish line in the Florida Derby, but he wasn't running away to the finishline), so if he gets trapped in behind horses until the eighth pole, he might lose all hopes of winning the Derby. And if this analysis of the horse is correct and the "extra furlong [is] no problem for him," he almost certainly cannot go the 12 furlongs of the Belmont... Big Brown's sire was a sprinter. Scat Daddy last year managed to stretch out his father's speed over 9 furlongs, but whether because of the extra furlong or because he got a little bit of a rough trip, he ended up among the last horses in the Derby. And remember how the great Holy Bull roared home in the Florida Derby in the same style as Big Brown (to finish in a faster time than BB too), only to flatten out on Derby day where he had no pressure in the race at all.
I doubt that Big Brown will win the Derby and he almost certainly will not win the crown.
How can I not like Big Brown in the Derby?
When was the last time you saw a horse win the Derby off of 3 starts? Unless you were alive in 1915 (unlikely), you haven't.
And who has Big Brown beaten? He won against maidens and allowance horses then won the Florida Derby. How good was the Florida Derby field? Elysium Fields was supposed to be good but was not. Majestic Warrior was good as a 2 year old, but hasn't been this year. Tomcito was good in Peru but hasn't shown it in the US this year. Hey Byrn came back to win a stakes against maidens (wow). Smooth Air is the only one in the field that you could even make a case for in the Derby, but I don't think anyone considers him to be one of the leading Derby contenders. I don't think the Florida Derby was a tough race at all. The way the pace set up, if there were any closers worth their salt in the race they would have run on in the stretch and at least challenged Big Brown. Big Brown finished the race in a good stakes time for 9 furlongs... the fastest of the pack finished in 1:51 or so on a very fast track. I wouldn't call that a very good stakes time... I wouldn't call that field a very good group of stakes horses.
I'm a big believer in experience. To deal with a 20 horse field over 10 furlongs for the first time, you need experience. Curlin lost last year because he didn't have experience. I firmly believe that horses learn more from rough trips than from easy races. You get rough trips from getting a lot of experience against other talented horses. Big Brown has never been tested against talented horses and has never suffered a rough trip (unless you count clearing the Florida Derby field at the first turn and then getting an easy rail trip for the rest of the race).
If Big Brown gets a good post position and breaks well then he could have no problem at all. If he draws outside, inside, or breaks poorly and has other horses around him for the first time in his career, I'm not sure he can handle it. And like I said before, if he's stuck behind horses until the stretch, I don't think he's as good of a closer as the others... if it comes down to a closing race with Big Brown and Pyro or Colonel John starting from the eighth pole, I don't see Big Brown winning the race at all.
And think about the Florida Derby. We've heard that Big Brown can set the pace or lay off it in a stalking position. In the Florida Derby he had to go up and set the pace... had he tried to get into a stalking position he would have been 3 wide for the whole first turn. Luckily for Big Brown, no one else wanted to set a very quick pace so he easily circled around the field and went up for a leading rail trip. In the Derby, even without War Pass, there will be significant speed. Bob Black Jack has great speed (he set a world record!), Gayego has speed as does Tres Borrachos. Cool Coal Man has speed or can sit off the pace. If Big Brown draws outside on Derby day, he could be 4 or 5 wide on the first turn. And there's enough pace that he might not be able to easily clear the field and cut to the rail... so he could be forced 4 or 5 wide for the entire race. In that case, he's going to run considerably more distance than the 10 furlongs (which is already a question with a sprinting sire). And the quick pace would have set up a closer, especially one who got a rail trip like Street Sense did last year.
I admit that Big Brown is a decent horse and I think he'll develop into one of the better stakes horses this year. And there are circumstances in which Big Brown could win the Derby. But, given his career with only 3 starts including only 1 stakes try, I don't think he's experienced enough to overcome trouble to win the Derby.