Could be, but I always thought our response to nuke was supposed to be all-out retaliation...hence, MAD.
Yes, MAD is/was part of the plan:
We first had massive retaliation (you hit us, nuke or not, we don’t care, we will simply nuke you); then proportional response (you hit us then we respond in kind, in proportion to the type and severity of the attack); then MAD (exclusively a USSR/US balance of terror type of thing).