I'd wager possibly so, in both the late to early 50's and in the 80's, especially towards the end of the decade. The period inbetween was more absolute in using nukes off the bat, especially in 1962 during the Cuban Missile Crisis. Although technically it is possible to fight such a war with little to no nukes, at least for a period of time, depending on the POD and whatnot.
And yet on that note, I find the notion of calling a war between NATO and the WarPac if it is just between those two, "WWIII", to be misleading, especially when I was thinking about such a war in the likes of Red Storm Rising, but maybe it's just me.