Short answer..no.
Your guys are still tankers , and would wear their Branch insignia , realistically, only the ossifers would be wearing them in the field. Enlisted smhucks would only wear their branch insignia officially when in the variations of the Class A uniform.
Don't know if it would have happened back then, but I have known quite a few of us modern enlisted , at least in the Cav , would wear the Crossed Sabers somewhere on our uniform, usually under a pocket flap or cloth subdued insignia sewn onto our Patrol or Boonie caps. Simply a esprit des corps thing.