Absolutely. People always forget how population migrations can bring down empires.
What do you expect these climate refugees to do? Die quietly? "Well, we earned it, not being born into wealthy societies. We've got no one else to blame but us"?
Get real. There will be strive and conflict and war, and everyone (lookin' at you, China, USA and Russia) will still be playing the 'Great Game' and try to one-up the other ones, even though survival is at stake.