Arizona Gov. Evan Mecham sat silently through the opening session of the Republican Governors Assn. in Santa Fe, N.M., despite earlier speculation that he would ask the governors for an expression of support in his troubles at home. Mecham is the object of a recall campaign and a grand jury investigation in Arizona. Before the start of the formal sessions of the annual meeting, Mecham told Michele Davis, executive director of the GOP governors, that he never intended to ask for a vote of confidence from his fellow governors. Republican Party Chairman Frank J. Fahrenkopf Jr. was at the conference for a closed luncheon to discuss drafting of the 1988 party platform. Frank Donatelli, the White House chief political aide, also was scheduled to meet with the governors.