Definitely not. It may go through a bottleneck in which humanity has to adapt or die (not for the first time, I might add), but (if anything) after the climate has stabilized and life has adapted it will be more fecund than anything -- all those new shallow seas will be totally awesome biomes.
It will take millions of years to recover from the biodiversity loss we've already put into motion. Hundreds of thousands, millions of species that just don't exist anymore. The intricate relationships from parasitism to symbiosis and everything in between, a vastly complex machine we just stomp on, cut up, blow holes in. Yep. That machine will be fine, shame about those eyebrows though.