Yes, items procured by foreign partners under cooperative programs must also be reported to the DoD IUID Registry when the items are delivered and will be accountable to a U.S. Government contract.  If the items are purchased with U.S. dollars, they must be reported in accordance with IUID regulations.  All new procurement requirements are based on DFARS 252.211-7003, Item Unique Identification and Valuation, as prescribed in DFARS Subpart 211.274.   A great resource for all things IUID is the procurement toolbox.  https://dodprocurementtoolbox.com/cms/faqs/iuid-faqs

Also, depending on the specifics of the items to be marked, often the cost of adding a mark is relatively small compared with the cost of the items. If so, there benefits to adding the 2D mark and submitting to the IUID Registry. The UII provides a globally unique identifier no matter which country holds the equipment. Plus, the UII lasts for the life of the equipment, which means it is “DoD friendly” if it ever is transferred (even temporarily) into the US DoD system.