Lets see: Austria sends its small fleet off to a realatively distant port, where that fleet will not have long term logistic suport, and leaves its coast defense weaker. I suspose that this resulting control of the Black sea might allow amphibious ops on the Urkranian or Russian coast. Assuming Austria has any practical amphib ability.

Although small, Turkish navy had logistical support and amphibious ability which was demonstrated in the Balkan Wars.

To make it worth moving the Austrian fleet some sort of large stratigic advantage needs to be gained. Small operations dont change the equation. Perhaps if this Austrian fleet allows Odessa or Sevastopol to be captured in 1915 then the consequenses will be worth it.

As it were: It is surprising so little the Turkish navy achieved in the Black Sea. The Goeben and Breslau should have swept the russian away.

Goeben brought a short lived limited superiority to Ottoman Navy. But then Russian Navy builded several Dreadnoughts (I remembered 4 but need to check) at Black Sea. Then Russian navy had complete naval superiority. The all Ottoman navy could do was raiding. Ottoman Navy did not have a shipyard. They could maintain and repair their ships but could not build a new one.

The Austrian ships would probably have been less useful to the Central Powers if rebased at Istanbul ... the approaches between the Black Sea and the Mediterranean were already well-guarded by artillery and mines, and they could never really have come out and taken on the British and the French.

Instead, by remaining at home, they could do nuisance raids and U-boats were able to operate in the Med from the Adriatic ...