I've heard this line of thought - that Christians should read Nietzsche and can learn from him from two thinkers, Merold Westphal and Bruce Benson.
Neither would say Nietzsche is generically sympathetic to "Christianity." As Jo points out, Nietzsche has a pretty polemical attack on "Christianity" inter alia.
As far as I gather, the main way this works is to keep the quotes around Christianity and maintain that what Nietzsche critiques and does well is something like cultural Christianity or Christianity with its own idols (often masked in the guise of piety and other religious elements).
Obviously, this strategy is going to face problems with Nietzsche's views on things like the resurrection. But I think it works pretty well with the "god is dead" passage in Thus Spoke Zarathustra insofar as part of the point there is to critique a godless society that keeps talking about God (whether the critique is then supposed to say the idea of god has always been stupid or merely that it's stupid to hold onto the idea when no one believes I don't know).