Do you mean during the Twilight War?
If so, I think the answer is yes.
The War Powers Act of 1973 put limits on how presidents can use the military overseas without a declaration of war by Congress. Yes, every president since has pretty much ignored* it, and Congress has let them all get away with it, but I think the Commander in Chief's powers to direct a total war (like WWIII) would be seriously hampered without an official declaration of war and all that entails.
A declaration of war might also be a requirement of NATO protocols, but I don't know.
*The US hasn't declared war since WW2. Not in Korea, Vietnam, either Gulf War, etc.
Granted, none of those conflicts qualified as total war (full wartime mobilization of the military and economy).
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