Unless I misunderstand your argument and premises, this is not true. Evolution does not require death. All it requires is that a genetically coded attribute be preferentially reproduced.

As an extreme example, assume an organism is born that has a genetic mutation that causes it to be unable to reproduce. It does not require this organism to die for it to fail to pass on that attribute.

In a less extreme example, assume "twin" anteaters are born. One has a significantly longer tongue than the other. The one with the shorter tongue isn't in danger of starving, but it does take him a lot longer to forage than his brother. While Shorty is still at the dinner table, Longo is out carousing with the lady anteaters, passing on his long tongue attribute. (Incidentally, the ladies really like his long tongue regardless of its ant-extracting abilities. This probably doesn't help Shorty out very much, either.) A few years go buy, and Longo is paying child support for a dozen kids, all from different mommas. Fortunately, Longo's ant-foraging abilities make him able to keep all those kids' tummies full. Meanwhile, Shorty has settled down with his one special lady and they have a kid together. A very nice little nuclear family. But the Longos outnumber them nearly a dozen to one. And in a generation, it will approach a gross to one, and keep expanding geometrically, even if none of them ever dies.

So: TL;DR summary: evolution functions on preferential passing on of genes, not the death of those with worse genes. Death is not required.