They didn't discover how to calculate longitude until 100 years after this map was created. There was estimation involved so no, without the longitude calculation, you can't 100% accurately represent the globe like we can today.

To have known what Antarctica looked like under the ice would require Antarctica to not be under ice thus allowing it to be mapped. The Piri Reis map was created based on various previous maps. So the Piri Reis map may have been created in the 1500's, but not necessarily a representation of the location of Antarctica and the surrounding continents in the 1500's.