The NCAA and NJCAA (and other JC sanctioning bodies) are separate organizations. Considering only the rules, and ignoring any ethical issue, a player who has signed a LOI to a JC may choose to attend a NCAA or NAIA school instead.
If a JC player was a qualifier, he may transfer to a NCAA school after his first year. Besides the academic requirements, he does need to have registered with the NCAA Clearinghouse in order to be classified as a qualifier.
Mid-year transfers to a D1 are not eligible until the following academic year, so it is only practical to transfer at the beginning of the fall term.