Not really. Even RCP8.0 wouldn't lead to extinction of the human race.
Aka migration causes war X which due to _ spiraled into WWIII. Granted the world without global warming could alos end randomly as well so you can just say unknown unknowns are always a risk even if it does mean a slightly less stable geopolitical environment that does not nessisarily mean anything terrible happens.
you do realize that initiating nuclear war is suicide, right? the u.s. took advantage of the only chance of actually using one because they were the only nuclear power at the time.
Given there are plenty of suicidal humans, that's not entirely comforting.