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No, while within the country that issued a residence permit (or D-Visa), the 90/180 clock does not count
Citizens of Australia, Israel, Japan, Canada, Neu Zealand, South Korea and the United States (who may apply for residence inside Germany), will be issued a Fiktionsbescheinigung after such an application.
Allthough this cannot be used as a visa replacement to cross the external Schengen border (citizens of these countries don't require a visa), it is still a residence permit and the days inside Germany don't count for the 90/180 days rule.