No, but Russia can hardly kill more than 5% of NATO population even if it fires all munitions it has, to the last one, on cities.
The casualty calculations are squarely in NATO's favour.
Since when do nukes target "population" and since when is it a success metrics of a nuclear strike?
Nukes target industrial and economic centers. Both NATO and Russia have enough nukes for at least 1% to bypass missile defense end ensure mutual industrial and economic collapse.
Most of the global population would likely survive, it's just that there won't be any NATO or Russia anymore, just random tribes of survivors.
Maybe we can be ok with just having Lisbon or Munich or Lion incinerated instead?