ISTR that _Swordspoint_ by Ellen Kushner had no religion (or magic, for that matter) whatsoever. Any religion that was there stayed very much in the background. (The companion piece _The Fall of the Kings_ has both magic and a variety of cults/extramural religions, but TFotK is an odd duck for a lot of reasons.)

So, I'd say it's perfectly doable.

(Swordspoint is a virtuoso piece of fantasy writing and worldbuilding in any event, and certainly worth your time.)