Yes, it happans, I met my now fiance on Carnival last year. I was on my 4- day cruise with my mom and saw this gourgeous guy working there. I think that from the first time we looked at each other's eyes, we knew that we ment for each other. We didn't have chance to talk much because he was on duty but we secretly exchanged phone numbers. Those 4 days on the cruise went very fast and we had no chance to even talk, crew members are not allowed to talk to passangers! Anyways...........he was on his 8- month contract with Carnival and we wanted to see each other again one day, so we decided that I would go see him on Catalina Island one day where they stop for couple of hours. So we saw each other every Tuesday for a year on Romantic island of Catalina, believe it or not. His contract ended on February 28th this year and now we are together making plans for future.
So, yes, it's possible to meet someone and fall in love on board.