When the Surge Protector is at end of life will the fixture turn off?

No. Only surge suppressors specifically intended for being wired ‘in series’ will turn the fixture off at end of life. Hatch’s LSP series of surge suppressors are not designed for and not intended to be wired in series. Instead, Hatch’s LSP3 series of surge suppressors is available in a model that has an end of life indicator LED that can be used to detect when it is time to be replaced, but in a typical parallel-application, power to the fixture will not be interrupted.