Formally, the U.S. did maintain an embassy and ambassador in the Empire (Fun fact: one of the last ambassadors was Henry Morgenthau Sr., father of the future Secretary of the Treasury for FDR). I can not, however, speak for the quality of the diplomatic relationship, just that a formal one did exist. Informally, several U.S. businesses operated in the Empire, neseccitating some level of bureaucratic cooperation to grant licenses and the associated paperwork. The one I am most familiar with is Standard Oil. They had several representatives buy up land in the Negev as potential oil fields. The issuance of valid, at the moment, titles and deeds means that the government, or at least the bureaucracy, shows at least some level of cooperation and tolerance, though this may have been out of Ottoman desperation or Standard Oil duplicity. Sorry for any typos; phone.