G.B.
In my experience you must have a Masters to teach at Community College or Jr. College and a full doctorate to be a full professor at University.
The non-degreed teachers are usually master's/doctoral students that have Stipends that are in lieu of financial aid. They work as part of the funding and are under the supervision of a full professor. That Professor has the job of overseeing their class schedules, helping them make the tests and grading guidelines, etc....
If you are trying to become a College Professor then I would think enrolling in the program you are going to teach would be the best way to teach within that program. For example, if you wanted to eventually teach at a University level in the Mathematics department then you could enroll in the doctoral or Master's program and apply for a stipend to help with finances and then you would get all the teaching experience you need teaching beginning and Intermediate algebra, maybe even some other beginning level classes. Once you gain educational and teaching experience they would put you over more and more classes.
At least this is how it worked with my friends that are teachers at Jr. college levels or professors at university. One is a MSW/Ph.d in the Sociology Dept. and the other is a Professor in Mathematics.