According to this article and others cited by it, the tiara existed. There’s an interesting discussion of what happened to it toward the end of the paper.

The tiara seems to have been taken apart. The four crowns were detached from the helmet and “probably melted down,” but the helmet itself “almost certainly” ended up in a Bavarian treasure vault. The author suggests that the stripped-down helmet was gifted to Ferdinand I of Austria after the Truce of Adrianople. The helmet could have reached Munich through Ferdinand’s daughter, “who represented the House of Hapsburg in Bavaria as Duke Albrecht V’s wife.” In any case, a ca. 1550 depiction of the helmet appears in a collection of drawings that inventoried the Bavarian jewelry collection. Source:

Necipoğlu, Gülru (1989) - “Süleyman the Magnificent and the Representation of Power in the Context of Ottoman-Hapsburg-Papal Rivalry”

The article is in the first link above—check out p. 416 (17 of 28) for the discussion of the tiara’s fate.