Greece would not be amused, as Wilsonian Armenia conflicts with the region known as Pontus (particularly in the Trabzon area), which proponents of the Megali Idea had hoped to include into the new Greek state. (OK, so there was the Republic of Pontus - it could have been the first step.) Plus - how is the US going to supply the Armenian mandate and not let it over-run by the USSR, aided by local Bolsheviks, and/or Greece and/or Atatürk's crew? You're only going to get that if the US already has a mandate elsewhere in the Near East, which means King-Crane has an effect where, except for Lebanon (to keep the French happy - maybe except the OTL former Israeli Security Zone strip up to the Litani, to reduce some of the tension), the US has a mandate in Greater Syria (aka what we now know as Syria + OTL Israel, West Bank, Gaza Strip, Jordan, and the Çukurova region of modern Turkey and adjacent areas of the Aleppo Vilayet which became part of Turkey, such as Antep [modern Gaziantep] and Urfa [modern Şanlıurfa]) which could serve as a base from which to supply the Armenian mandate - even if the supply lines go through Iraq, with British consent, to make accessing the Armenian Mandate easier.