It is difficult to answer that question categorically. They are certainly infatuated with each other, as the imagery of their speech would testify. Romeo, for example, eschews conventional religious references in his praise for Juliet's beauty preferring to compare her to the stars and moon in the sky above them (Act 2, scene 2). Romantic? Most certainly. Lasting? possibly, but this is a peripheral issue in my opinion.
Classical tragedy (in the Aristotelean sense) centres on the tragic flaw (hamartia) of the main protagonist - the hero. In R&J, we are presented with two main protagonists, a 'pair of star cross'd lovers' who are fated to die for their love (see Prologue). Their flaw, which to a large degree they share, is that they love "not wisely, but too well" to steal from Othello. Classical tragedy also requires the hero to die, after a period of pathos and catharsis in the audience, who forgive him for his fault. In R&J, the audience certainly pities the lovers, but also bemoans the impetuous nature of their love. It is necessary that they die to maintain the integrity of the tragic plot, in other words.
We are presented with an all consuming passion, that burns both characters up; they cannot survive whilst they are apart. And because of the history of bad blood and emnity between the families, they cannot make their love known for fear of reprisal from parties within their families; Tybalt, for one, hates peace.
The secrecy and urgency of their relationship is a reflection of both the intensity of their feelings for each other, but also of their youth, and it may be this consideration that would persuade most people to suggest that it might not last.