Probably not. I would hope that most of everyone would still be tucked away until the dust settled, and Hulk should have returned to Bruce by then, so not many eyes should have bared witness to Bruce at the site of the invasion.
Of course, Bruce's colleagues may have sufficient grounds to suspect him of being the Hulk. Basically any one close to him would have noticed his disappearance, and would correlate the giant green gamma monster with Bruce's work on radiation and biochemistry.
Oh and pretty much every government entity would probably know, since Bruce was basically made public enemy #1.
The strongest case for the world knowing that Bruce is the Hulk is after Winter Soldier, in which Natasha leaks a lot of classified SHIELD info to the internet. If Bruce was among those files, then the world probably knows.
Now would anyone on the streets immediately recognize Bruce? Probably not. He's not as high profile as Tony for instance. I think Bruce could still blend in with the masses, and to someone not actively searching for him, he'd just be another face in the crowd.
