Greece would be better of than it is now. EU is raping Greece right now.
Projects like the Trans Anatolian pipeline, South stream, BTK-Railroad that eventually will connect China with Europe via Railroad will bring the East closer to the West. Georgia, Azerbaidjan, Pakistan, Afganistan, Iran and Turkic states will benefit hugely from this.
The "Silk Road" could become a great Geopolitical Advantage for Turkey to Connect Balkan and north African Economies with Eastern Markets! Spain and France could lose some Influence in northern Africa. And the newly formed Union will bring stability in the Mid-East. Greece would be the logistical point and the gateway to the West (Europe) If we share the newly found resources and settle with the history we can make this happen. We will form a new block against other powers. Greece would become a strong and rich country. Greece deserves to be in a better position than it is right now.
As for Armenia: I dont believe Armenia will have a choice. It is already isolated by Georgia, Azerbaidjan and Turkey. Iran is their only gateway. BTK railroad let to more Armenia isolation.
The president of Azerbaijan, Ilham Aliyev in 2005 reportedly declared, "If we succeed with this project, the Armenians will end in complete isolation, which would create an additional problem for their already bleak future." Armenia has a decreasing economy and population. So you dont know were they will stand after 10-20 years.
That last point you made grabbed my attention. Turkey already draws attention. See for Putin who visited Turkey to boost energy deals and economy.
Dont underestimate Turkey. We already have made moves (soft power) After Assad is eliminated who will rebuild Syria? the answer is Turkey my dear friend. The new leader will be pro-Turkish. As for Bulgaria. The third party is Turkish. The region i mentioned in OP is full with Turks. They dont have seperatism, but if Bulgaria will ruin their economy more, people will be drawn to this union by themselfs.
A lot of things that can happen in a short time span. Again we already have soft power in these countries. A economic and social union could be posible, but Turkey needs more improvements. We should fulfill the role that Germany has in the EU in this newly formed union.