League of Legends (LoL) Question: Is Nashor's Tooth effective on AP Ezreal?

If you do not need mana because you have constant access to Blue Buff, buy this item for the 20% CDR and gain the proc as a bonus.

Can you build it on AP Ezreal? Sure.
Are other items simply better on him? Absolutely.

Nashor's Tooth is a very niche item, that works well on AP champions that rely on AAs to do damage, like: Kayle.
As AP Ez you will rarely find yourself using auto attacks and the Nashor's Tooth's passive only works with Mystic Shot.