Do you think the cold war would go to an allout war if nukes never where invented?

A few weeks ago it was 70year since the bombing of Hiroshima and Nagasaki. This started talks about banning nukes and calling out for a world wide nuklear dissarmement.

But lets flip the issue, do you think that if not for the nuklear treath the cold war could have escelated to a full blown WW3? If so nukes may have saved more people than the polio vaccine.