Very likely, yes.
The primary wagon route south through New Mexico varied as to which side of the Rio Grande, but generally followed the route: Ft. Union, Las Vegas, Raton Pass to Santa Fe thence to Albuquerque, Los Lunas, La Jara, Socorro, San Marcial, then very east of the river through the Jornada del Muerto to Mesilla.
At Mesilla, it would have likely turned west and traveled along the former Butterfield trail to Ralston (near current day Lordsburg), then headed northwesterly on the wagon road to Clifton/Morenci.
Likely never passed through Silver City proper, but about 30-40 miles south through Grant County locations such as Old Mimbres and Soldier's Farewell.