Not necessarily. That's the entire point of US American nuclear weapons.
Edit: Unexplained downvotes are hopefully for my unclear wording. MAD is the doctrine of the US, but other places have doctrines ranging from "don't disturb our geopolitical sacred cow" to "escalation in armed conflict." Obviously there's reason to wonder whether everyone, pushed hard enough, would resort to nuclear weapons (an important consideration before putting an enemy on 'death ground'), but having stated policy that the weapons are not on the table is better than a stated policy that use would be justified “… also in the case of aggression against the Russian Federation with the use of conventional weapons, when the very existence of the state is put under threat”, as Putin signed in 2020.
That's the entire point of nuclear weapons, isnit?