We cannot definitively prove Romeo and Juliet would have gone to hell because we would first have to prove heaven and hell exist and, thus, that a particular god exists, a god who decides which people go to which place. What we can prove is that, according to the religion Romeo and Juliet appear to practice, the common belief is that they would have been bound for hell.
Set in Italy in the late 16th century, we have reason to believe that the characters would practice Roman Catholicism. Further, the existence of Friar Lawrence (a Catholic cleric), as well as his prominence within Romeo and Juliet's lives seems to indicate they are Catholic: Romeo routinely goes to the friar for advice, and Juliet goes to the friar's cell to be married to Romeo under the pretext of needing to go to confession, a Catholic practice. For Catholics, the act of taking a life — any life, including one's own — is a mortal sin; they believe that one's life is the property of God. By destroying that life, one wrongly lays claim to something that belongs to God. Since Romeo and Juliet are Catholic (as would their families and, most likely, community be), they would believe that taking their own lives is a sin that would send them in hell.