Well, it would not have been an official alliance...they would have just put the German soldiers in Allied uniforms under Allied officers, I would assume.
The same sort of thing happened on the Eastern front in 41-45 when many thousands of Ukrainians and other former Soviet troops joined the Axis forces to fight Stalin, for example.
But one thing for sure, the western public and soldiers were longing for peace by 1945, and they would not have been happy at a continuation of the war. This would have made no difference, however, if the Russians had launched a full scale attack on the West. Then things would have taken their inevitable course regardless.
Stalin was entirely treacherous and ruthless enough to do it, if he thought he could win. He cynically attacked the Japanese in the last few days of the war, hoping to grab some more spoils in Asia before it was over.