Being a Caliph is not exactly like being appointed as a Pope. If you had a significant military power, you could declare yourself whatever you wanted. It was more of a matter of being able to have claims on the traditional Muslim territories.

As for your question, he probably wasn't revered as one outside the Turkish borders. Ottoman Sultans didn't really get to be accepted as caliphs until Selim I conquered the Mamelukes and destroyed the opposition.