No, it will not. This module is designed to plug into a M.2 (Type A or E) connector. Your NUC, on the other hand, has the older M.1 connector. The top Intel solution that plugs into your NUC is the Dual-Band Wireless-AC 7260 (7260HMW). Here is link to this card on Amazon: https://www.amazon.com/Dual-Band-Wirless-Bluetooth-PCI/dp/B01E85QIFI.
Hope this helps,