Yes, it's possible. I used to be in a relationship with a guy who was an ESL teacher at one of the schools in my city and he taught Koreans and Japanese (mostly girls too). At one point last year, he admitted to liking 3 girls in separate times, although he said he didn't do anything. Although the last girl, he seriously liked enough to have a special pet name and to even consider pursuing her. He was young, 22 yrs old, with the girl just a few years older than him. Personally, even having those feelings in the first place is so wrong and unethical. As a teacher, one should draw a line between your personal and professional life. Sure, it's good to make the students like you, to become friends with them, but only at a professional level.