I didn't want to imply that I was sure that this would be the outcome. You are right about the dynamics of the Islamic conquests, of course. BUt consider that IOTL, the Umayyads only had to deal with half the Göktürk Empire, which had lost its momentum and was splintering under the consequences of Chinese meddling. Before the split, the Göktürks were good candidates for the title of the most dynamic power in Central Asia. And they don't have to defeat the Umayyads the way they were defeated by them IOTL - holding the forts would make quite a difference already.
Are we assuming that the Chinese empire in this tl does not take any interest in the west? I can imagine denying conquest, but do we come to the view that the Sui or this altered Tang simply neglects its west, despite the obvious wealth to be had from Tocharia? It was not so far from the memory of the Tang period, the venture of the Han dynasty toward the Xiongnu and the rise of the Kushanshah, allowing the creation of the flourishing Silk Road.
If we assume that the Sui or altered Tang, still take an interest in the steppe, what is stopping a punitive attack by China in connection with the Muslim invasion? Does the Celestial Turkic Host have the staying power to withstand such a barrage? It also should be remembered, the Tibetans still exist, how doe the Tibetans face a world without the Anxi Protectorate? An interesting question, perhaps a more intense Tibetan focus upon its wars with the Umayyad and later Abbasid (which during the Abbasid were not so dramatic, the Tibetans and Umayyads crossed swords far more).
I know this is a little later than our target time period, but it's worth considering: A few decades before the Battle of Talas, the Gokturk Khaganate was receiving thousands of pieces of silk in tribute (sorry, trade, with the exchange rate being approx. 100,000 pieces of silk for 30 horses) from China and yet it still crumbled almost completely after Bilge's death. Why? Because the Turkic empire was fragile - it was a confederation based on shared interests and the moment anyone had a chance to break away, they almost invariably did. It didn't matter how much success their Khagans had - as soon as anyone smelled blood in the water, it was over - either the rebels lost and were forced to submit, or the Khaganate was over.
They were bought off when they were strong and beaten hard when they were weak. As far as I can tell, the Gokturk focus was always a little bit more pointed Chinaward. And, like John says, the Chinese always had a huge incentive to bribe and cajole and otherwise try to control the barbarians. So you've got two potent factors here - a politically weak (and economically vulnerable too, if the constant famines of the era are anything to go by) but military strong nomadic state and the rising Umayyad threat in the west, and they're always going to be back as long as someone needs loot and victories.
Circa 625, the Gokturks annexed Tokharestan and Gandhara, at the time basically Indo-Hephthalite kingdoms. No more than a generation later, they're pushed out by the Umayyads under Al-Ahnaf ibn Qais and Abdallah ibn Amir - whose conquest lasted as far as I can tell about three years before the Gokturks were back for another generation, and all this while the Turks are being turned against each other. Well into the 8th century the matter was hotly contested. The Arabs keep having to send armies up into the region and those armies keep getting mauled or looting, but either way failing to establish permanent footholds.
The Umayyad, as I can recall, definitely struggled in Central Asia in the early days - these conquests were far harder than their comparative steamroll through the Near East and North Africa. However, those invasions weakened the Turks immensely. I'd even go as far as to say that they probably played a role in China and Tibet's ability to rise just as much as they did for the Arabs. All these new up and comers - the Tang dynasty, the Umayyad dynasty, the Tibetans, everyone benefited from seeing the Turks knocked down a peg. So if China is distracted for whatever reason, I have to concur - I think you're going to see a stronger and more dynamic Tibet.
If China doesn't replace the Gokturks in their sphere however, you're more likely to see Central Asia become a battleground of local Turkic, Tibetan, Hepthalite, Indian, Sogdian, Arab, etc. factions who all want a piece of the pie. This was devastating in OTL. It could be even worse here.