Like most things, it depends. The FAA definition of 'approved' is found in FAR 1.1 -
"Approved, unless used with reference to another person, means approved by the FAA or any person to whom the FAA has delegated its authority in the matter concerned, or approved under the provisions of a bilateral agreement between the United States and a foreign country or jurisdiction."
So just because the check airman is authorized by XYZ CAA to do pilot checks doesn't necessarily the check would count. But if they hold a FAA instructor rating or the training center also holds FAA authorization they would. Or if there is an agreement between the FAA and XYZ CAA.