I'm not convinced about it...
1) The Turkish armed forces received weapons shipments from Great Britain, and U.S. but also from Germany.
2) Also just before the onset of hostilities the Turkish navy underwent a program of expansion and modernization: two submarines and four destroyers were ordered for construction in U.K.,
two submarines were ordered for construction in Germany.
3) Thanks to British and French shipments one air regiment, along with five independent air wings, was formed in 1941. Shipments of military equipment from Germany replaced the shipments from Allied countries in the same year: in 1943 the Turkish Air Force consisted of 6 regiments, which included allied airplanes (like Hawker Hurricane.IIB and C and Bristol Blenheim.I) and german ones (like Focke Wulf FW 190A-3 and Heinkel He 111F-1... superior and newest!)
4) the anglo-soviet invasion of Iran, on August 1941, was a warning for the Turkish government (soviet troops advanced from Adzerbaigian to Maku e Khoi, few kilometers from Iranian-Turkish border...)
5) As sustained by P.Carell in his "Operation Barbarossa", from the conquer of the Black Sea ports of the west Caucasus (Novorossisk, Tuapse, Soci, Suhum and Batum), there had been the Turkish "axis-conversion".
6) Surely, as reported by W.Churchill in his book "The second world war", on August 1942 (before the first battle of El Alamein) and on January 1943 (after Stalingrad and the second battle of El Alamein) the position of Turkey was different..., but however the "allied-conversion" of Turkish government was prudent (also in 1943!!): Turkey was warried about the imperialistic politic of Russia, but it was surely linked with USA/UK... but that does not mean an "allied-inclination"...