Is it possible to be a recruit and not get an OV? Or do all recruits get official visits.
There is no OV requirement to be recruited. There are a lot of recruits that make their verbal commitments well before the OV can take place.
All people who are offered official visits are recruits, but not all recruits are offered official visits. Students become recruits essentially when a coach makes an effort to personally contact the student away from the campus. Becoming a recruit is just the first step on the ladder though, and there are several steps between that and receiving an offer.
Be careful though of thinking there is a cast in stone, linear progression through the process. Recruiting is often fluid and variable.
As Varska said, some recruits receive an offer of support before an offer of an official visit. Actually in my experience most recruits only visit places where they have already received an offer, likely because they are limited to only 5 official visits. Other people and other sports may have different experiences.