It's possible, but it hasn't happened in my case. In my first job, I was offered it the following morning. In my current job, I heard a few days later.
Sure. I was offered my position at the end of my interview, but I'm a para. I'd say it's very unlikely for teachers in a saturated market unless you have some kind of connection and the interview is just a formality.
This was just my experience a couple of weeks ago, but I'm already a teacher in the district and my principal made a call on my behalf to set up the interview. My other two job offers came the day after the interviews.
For my first job offer, I was offered it on the spot. The P really liked me, and he two different openings at his school. He told me if I accepted his offer, he'd guarantee me one of the positions but told me he wasn't sure which one he'd give me yet. He asked which one I'd prefer and told me he'd call me later that day and let me know which position I was being offered. I think this situation is very unlikely and haven't heard this happening often, although I do know of one other friend of mine who was offered a position on the spot as well. Generally, I think they like to interview all the candidates, check references, and possibly call back for second rounds before offering positions on the spot. My second district didn't offer me the position until about a weekish after I interviewed.
My wife was offered a job at the conclusion of one of her interviews. (It was her first choice school, so of course she accepted.)
I got a call about an hour after the interview. They finished interviewing the other candidates and then called me to offer the job.
I was relocating from another state. I hadn't even made it back to my hotel when they called with a job offer. Of course, that was during a teacher shortage. It'd be very rare now unless they have multiple openings.
My Teaching Assistant position was offered to me right after the 45 minute interview, even though I was told by the Kindergarten Teacher AND Principal who both interviewed me that they were going to interview other candidates and then get back to me... Well, I only made it to the hallway-----------walking out to leave the building after the interview and they both ran out after me..LOL..and they offered it to me! Its been the best job I've had so far I just love Kindergarten!!!!!!