To my knowledge, no. From November 1914 onwards, the war against the Ottoman Empire was almost entirely waged by the Russians and the British, the latter making extensive use of the British Indian Army and later recruiting Arab allies, the former dropping out of the war in March, 1918.

The United States didn't become officially and fully involved in the war until April 1917, and the first US troops didn't begin to arrive on the continent of Europe until late 1917. American units saw service in Italy and France, and were later involved in an abortive Allied expedition against the Bolsheviks. If ANY American soldiers/sailors/airmen/marines DID in fact see combat against the Ottomans, it was probably not a significant number. Besides, by the time of American entry, the Empire was already on the ropes.