Romeo, it seems, was quite adept at falling "quickly and heavily" in love. Much of the first act of the play is devoted to Romeo's sufferings because he is in "love" with Rosaline. The cause of his suffering is her complete unwillingness to return his "devotion." And yet, a few short moments at the party which he and his buddies crashed, Romeo has fallen in "love" with Juliet. I think that had the course of their relationship played out, that Romeo would have fallen in love with someone else after Juliet.
It is plausible that the two of them would have acted like that. After all, they are young and to be young is to be selfish and impulsive. If they were older, I would find this more incredible. But young people are great at convincing themselves that their own feelings are the most important things in the world and that what they are feeling is totally incomprehensible to others.
So I can totally see two people who are that young essentially going crazy the way these two do.
Why cannot the three days be metaphoric rather than realistic? After all, three is such a religious and significant number as it represents the Trinity and perfection and completion.
If, however, the three days are, indeed, exactly 72 hours, then, perhaps the whirlwind romance of "violent delights" may have been precipitated by the tremendous sense of urgency that Romeo and Juliet felt because they were romantically "truncated" by the heated feud of their two families.
Quite honestly, your question has to do whether one believes in love at first sight, ... or only infatuation at first sight. If you believe that love (and I mean TRUE love) can begin at first sight, then you believe a love story of this heavy magnitude is certainly possible. However, if you think the attraction is only infatuation (i.e. only physical love), then you believe a love story of this magnitude isn't possible.
Let me add a little wrench into my own little theory: obsession. Because young lovers can often get obsessive about each other, I suppose it would be possible for an obsessed and infatuated couple to go to those lengths. My, that would make Romeo and Juliet a depressing story, wouldn't it. Ha!
Let me add another little wrench for you to peruse: commitment. Why is it that arranged marriages in other cultures often last forever? Commitment. Why is it that you see couples married for fifty, sixty, even seventy years? Commitment. If these youngsters had a strong sense of that value, a love story of this magnitude is possible.
Because your question is about my opinion, I'm going to be an idealist and say that it CAN happen. I WANT to be able to say that it does. I'm remembering for a moment the similar revelation in Life is Beautiful (a totally dissimilar, although tragic tale of the holocaust). Call me a cockeyed optimist, if you will, but for people who fall in love that fast, ... God bless them!