Movie, novella, or stage musical?
YES
The audience that attended the theatre in Shakespeare’s time would indeed believe they were in love. A common belief at the time was that love can be caught like an infection. By breathing in love it infects you and changes you instantly.
Look at the characters in Twelfth Night. Viola, just barely survives a shipwreck, in which she thinks her brother died. But she sees Orsino and falls in love with him. Olivia, morning the death of her brothers, sees Viola, dressed as a man, and falls out of mourning and into love. Orsino, although he thinks Viola is a guy, starts to "feel funny’ about him. But the love infection is overcoming him. Olivia, doesn’t mind being switched from disguised Viola to her twin brother because, well, she’s infected with love.
Most Shakespeare plays deal with love and the different kinds of love. Romantic love, brotherly love, parental love (or lack thereof).
Given that bit, and Juliette’s dialog at the beginning, when her parents suggest marriage and falling in love with their choice, and she demurely says that she thinks, if she has to, that she can fall in love, if its at all possible … or words to that effect … If she can fall in love at parental command, why can’t she fall in love with someone who woos her from under her balcony?
Romeo is a poet, that was like, the ultimate intellectual aspiration for the time period. And he’s rich, she’s rich, they’re marriageable age – why not marry, try to reproduce. Odds are fair that it’ll work fine, and Juliette won’t die in childbirth, or Romeo of the plague, or the child of a childhood disease … 'tho not a guarantee this disasters won’t befall them, so there’s no point in wasting time.
Basically, if some modern pop star (cough - Taylor Swift) decides to pick up a random teenaged Kennedy, even if the parents don’t like it, who’s gonna stop them … and that’s a modern tale, with all the baggage against young marriage we’ve added in the interim centuries.
Asimov’s take is interesting. Consider – the priest is all for this plan, because he believes it will end the feud. This to our minds helps validate the premise. But consider: we assume the Catholic priest has a noble ideal (or at least I bought it), we accept that the time and place period accepts the priest as moral authority figure. But would Elizabethan audiences have accepted it as so? Or was that just another facet of the mockery of the romantic trope that Shakespeare has set up?
Weren’t arranged marriages still the norm in R & J’s time period? I always saw R & J as infatuated with each other. A passing fancy until they married whoever their families picked.
Or if we may rewrite your lines in properly versical form:
Romantic love
Brotherly love
Parental love
(or lack thereof)…