When one considers the factors that could have led to Ophelia's madness, I think it is quite clear that her madness is indeed real and not the least bit feigned. Her father first orders her to stop seeing Hamlet because he doesn't trust Hamlet's intentions and she cannot simply dally with a Prince unless he is going to make it legitimate.
Then, once she breaks it off, Hamlet tells her all kinds of crazy stuff about how he loved her but he didn't and urges her to get herself to a nunnery since all this love stuff is madness and all men are horribly wicked and evil creatures.
As if that weren't enough, this guy that she loved then acts like a maniac during the mousetrap play, kills her father, and then disappears to be sent off to England. The combination of all of this is enough to give anyone a nervous breakdown and when it is combined as well with her apparent suicide, it becomes pretty clear that her madness is all too real.