Considering the NCAA's definition of 'outside competition', a NCAA vs CHL series would be prohibited by NCAA regulations and Bylaws.
17.02.12 Outside Team. An outside team is any team that does not represent the intercollegiate athletics program of the member institution or a team that includes individuals other than eligible student-athletes of the member institution (e.g., members of the coaching staff, ineligible student-athletes, members of the faculty).
17.31.3 Exceptions -- All Sports. The following exceptions to the outside-competition regulations are permitted:
(a) High School or Two-Year College All-Star Contests. A student-athlete may compete in a high school or two-year college all-star contest during the summer prior to initial full-time enrollment in a regular term at the institution.
(b) High School Alumni Game. A student-athlete may compete in one game a year involving participants from the student athlete's former high school and its alumni team. In sports other than basketball, this game must take place during an official vacation period of the institution's academic year.
(c) Olympic Games. A student-athlete may participate in the official Olympic Games, in final tryouts that directly qualify competitors for the Olympic Games, and in officially recognized competition directly qualifying participants for final Olympic Games tryouts.
(d) Official Pan American Games Tryouts and Competition. A student-athlete may participate in official Pan American Games tryouts and competition.
(e) U.S. National Teams. A student-athlete may participate in official tryouts and competition involving national teams and junior national teams sponsored by the appropriate national governing bodies of the U.S. Olympic Committee (or, for the student-athletes representing another nation, the equivalent organization of that nation or, for student-athletes competing in a non-Olympic sport, the equivalent organization of that sport).
(f) Official World Championships, World University Games (Universiade), World University Championships and World Cup Tryouts and Competition. A student-athlete may participate in official World Championships, World University Games (Universiade), World University Championships and World Cup tryouts and competition.
(g) Multisport Events. A student-athlete may participate in officially recognized state and national multisport events