There isn't anything about Quantum Immortality that requires UDT (except in as much as any decision requires at least some kind of decision theory). The difficulty (and common confusion) is around translating primitive preference-intuitions into preference-beliefs about wavefunctions or branches. Once the values are given, both CDT and EDT will just result in the same decision that UDT would make (unless the specific decision also combines one of the other issues UDT is required for.)

I think UDT makes it possible to understand what decisions are, and how wavefunctions can depend on one's decisions. Before I came up UDT ideas, this was really unclear to me, and I had considered some other decision theory approaches where Quantum Immortality was sort of baked in. For example I had the idea that the wavefunction couldn't be changed, but when you make decisions, you're choosing which branch of the wavefunction your consciousness continues into.