No, they cannot. All the additional bylaws referenced are specific to the sports with exceptions. Wrestling has NOT established any exceptions to 12.8.3. Football has. You can play in up to 4 games and maintain a redshirt.
12.8.3 Criteria for Determining Season of Competition. 12.8.3.1 Minimum Amount of Competition. Any competition, regardless of time, during a season in an intercollegiate sport shall be counted as a season of competition in that sport, except as provided in Bylaws 12.8.3.1.1, 12.8.3.1.2, 12.8.3.1.3, 12.8.3.1.4, 12.8.3.1.5 and 12.8.3.1.6. This provision is applicable to intercollegiate athletics competition conducted by a two-year or four-year collegiate institution at the varsity or subvarsity level. (Revised: 1/11/94, 4/28/05 effective 8/1/05, 5/9/06, 1/16/10 effective 8/1/10, 7/31/14, 8/8/18 effective 8/1/18)