Harper's Bazaar, Fashionista and the Associated Press place Lady Gaga at The Plaza for the September 5, 2014 ICONS celebration and document her performance. This verifies an event, not a stay.
Lady Gaga performed at Harper's Bazaar's ICONS celebration at The Plaza in New York on September 5, 2014. Contemporaneous reports from Harper's Bazaar, Fashionista and the Associated Press place her at the exact hotel and describe the completed performance.
Source conclusion:
The cited sources confirm attendance at an event at the hotel, but not an overnight stay.