She was not the only European monarch to do so. Earlier, King Francis I of France is well-known to have sought an alliance with the Turks against their common enemy , Charles V (Holy Roman Emperor and King of Spain).
Certainly. The alliance formed by Francis and Suileman was extremely succesful. It lasted over two centuries, ending in napoleonic times.
It led to a much less succesful Hapsburg-Persian alliance. Charles V turned to the Persians in aid against the Turks. It certainly had a much shorter life span or success rate as the Franco-Turk one.