I think that the previous thoughts of being young are vitally important in answering this question. On some level, both of the lovers are so young and see this relationship as the only way to escape their own contingency or situation that entering the relationship almost becomes a necessity. In a social situation that is driven through family loyalty and family bonds, the two of them see their relationship as a way out. In this light, I think that the idea of being able to elude the constricting nature of one's familial predicament might be a reason to enter into this relationship with the other. Having said all of this, I think that I would have to feel mighty constricted by my current situation to enter into something that features so little in way of sustainable foundation or groundwork for real and lasting commitment.
This question has a lot to do with one's relationship with their parents. My parents were a little clueless when I was 15.
I probably would have tried to get things going because that was a pretty dramatic night! Hormones were indeed racing. What I would have changed though about the situation was the pursuit of marriage. Marriage is a huge deal. When I was 15, I would have thought that way too serious to deal with. So, I probably would have tried to sneak around in a dating relationship and before we got to the task of marriage, I would fess up to my parents about my secret love.
Keeping in mind that I am no longer young and am hopefully less controlled by hormones than people their age, no, I would not pursue a relationship with the other once I found out who the other was.
When you have only seen someone for one evening, you have not committed to them for your whole life. You can surely get over them pretty easily. So when the two of them found out they were from enemy families, they should have realized that it was not going to work out. They should have known it would cause more problems than it was worth. They could not have been so in love that they could not live with anyone else...