IOTL, at the end of World War I, Turkey was allowed a free hand in the Caucasian Isthmus after the Treaty of Brest-Litovsk and the Treaty of Batum, which stipulated that the Ottoman Empire was allowed freedom of movement of goods and persons through the territory of the modern Republic of Armenia into Azerbaijan. The armenians, however, ended up rejecting the further terms of the treaty, and resumed war against Turkey.
Eventually, the turkish forces were defeated at three major battles: Bash Abarn, Sardarapat (where a nationally famous monument currently stands), and Kara Killisse. Turkey lost contact with Azerbaijan and, within months of inconclusive fighting, sued for peace with the caucasians at the end of World War I.
But what if Turkey had managed to defeat the armenians, puppetize or even annex Armenia proper, and estabilish a link to Azerbaijan and Baku?
Could the sudden influx of oil into the Central Powers' supply help them through 1918?
For how long would Turkey be able to hold onto their gains in the Caucasus?
How does this affect the armenian genocide?
 
But what if Turkey had managed to defeat the armenians, puppetize or even annex Armenia proper, and estabilish a link to Azerbaijan and Baku?

Well, they kinda did.

When the Ottoman negotiators were informed of Armenia's last, desperate victories, they grudgingly reduced their demands on Armenia...by a tiny 400 square miles. This was the basis for the final treaty, which was signed within a week after the battles of Sardarapat, Kara-Kilise and Bash-Abaran.

The Ottomans got their connection to Azerbaijan; the Republic of Armenia was reduced to its minimal boundaries, partially occupied by Ottoman troops, and forced to grant transit to Ottoman troops and supplies across its whole territory. It became little more than the Ottomans' unwilling puppet.

It is true that the Armenian resistance slowed down the Ottoman advance towards Baku, so that might have happened sooner - but not, I think, much sooner.
 
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