One problem with the Gokturks: by the 600s and 700s they had a large Chinese population, who were a significant part of the aristocracy. So by your definition they are not pure Altaic.You have a point, but really, in the long run, Arab or Chinese culture has taken root amongst the Altaic people. A more unified Gokturk empire would have been interesting. As I noted previously, they fractured due to internal disputes and military setbacks. Now the question is *HOW* would the Gokturk Khanate stay unified and dominant?
In any case, nomadic empires like that don't have a very long lifespan...
There were some battles where the Umayyads beat the Gokturks in ~715. Maybe have the Gokturks win those battles, which would leave them in a stronger position. Barring ASB intervention, the state wouldn't last beyond 1000 , I doubt.