Could, but not likely (unless you believe the Soviet propaganda of the time).
I would not necessarily regard it as propaganda, though certainly the Cold War megaphone played it for all that it was worth.
Russia has been invaded many times and has a fundamental preference in its foreign policy toward maintaining a neutral zone, where possible, between itself and its enemies. The Soviets had a similar policy outlook; they viewed a neutral West Germany as a balancing neutral zone between themselves and the other Allied victors. When that neutral zone was lost, they consolidated their hold over the satellites.
During 1954, when the West German issue was a point of disagreement between NATO and the USSR, the offer was made to recreate the Joint Allied Council - this was refused. Then, in 1955, West Germany joined NATO, bringing NATO to the border of the socialist bloc. It was quite reasonable, I think, for the Soviets to pay attention to formalisation of their previously understood defence cooperation.