Uhh no. If you think being alone is all that makes Peter a tragic hero, you have grossly misunderstood his character and there's really no need for us to continue. As I just mentioned, most incarnations of Spider-Man nowadays reveal themselves to Mary Jane a lot sooner than he did in the 616 universe because most people agree that that was ridiculously drawn out. None of these Spider-Man's (namely the Ultimate version) become any less tragic because of it. If anything, they become even more so since now they have to worry about their lives as well as their own even more. Hell, even the new Spider-Man, Miles Morales, confided in his best friend, and he just took his first real step towards becoming a tragic hero in this month's issue. And are you forgetting the fact that Gwen Stacy is forever fated to die? So even this movie's Spidey isn't about to stop being down on his luck.
You act as if Peter revealing himself removes the tragedies of his past (abandonment, Uncle Ben's death, etc.) Is Batman any less tragic because Alfred knows his secret?
So your argument holds no water. If you prefer Peter keeping the secret completely to himself, fine. That's your opinion. But don't state it as a fact that it removes his status as a tragic hero when there is tons of evidence that flat out disproves this.