Does naegleria fowleri survive in tap water heaters that are chlorinated?

No: Chlorine kills it

Should not if: properly cholrinated. "Naegleria fowleri can grow in public and private water tanks and pipes, especially where little or no disinfectant (like chlorine or chloramine) is present. It can also grow in the pipes and water heaters of homes and buildings." REF: https://www.cdc.gov/parasites/naegleria/tap-faucet-water.html