The Arabian peninsula was under Ottoman suzerainty, except for the British South and Kuwait.
A surviving Ottoman Empire would formally incorporate Najd into its lands, IMO. Oman + South Yemen + Greater UAE are British administered, as well as Kuwait. The Ottoman Empire is the world's 3rd leading power during the *Cold War or whatever.
Actually, Kuwait was under Ottoman suzerainty too, but under British protectorate. When the Ottomans entered the war, the British declared it an independent state under British protection.
If the Ottomans hadn't entered the war, they would have consolidated control over Arabia, probably extending control into Najd. If they played their cards right, they could probably have occupied Kuwait, which would be of lesser importance to the British than keeping the Ottomans out of the war.
I don't think you'd see the Ottomans gaining any of the rest of British-held Arabia, like S. Yemen, Oman, Bahrain, and the Trucial States. But still, control over the oil of Saudi Arabia, Kuwait, and Iraq is not bad.
In this period, the interior of Arabia is dependent on the coastal areas for food and water. That's why the Saudis were fairly impotent when confined to the interior. With Europe embroiled in war, there'd be little trouble subduing the Saudis and obtaining mastery over the interior. After the war, the Hijaz RR could be extended down to Mecca and maybe even extended across Arabia to the Gulf. It wouldn't be all that difficult technically, but it wouldn't be very remunerative a line.
The Hijaz is not Wahhabi, and al Hasa is largely Shiite, so Wahhabism becomes a curiosity of internal Arabia.
As for Pervez' point, the Saudis occupied the Hasa in an opportunistic manner because the Ottomans were locked in the Balkan Wars and unable to stop them. I don't think this can be interpreted as a long-term loss of initiative. If everyone is tied up in WWI, you can bet the Ottomans would move back in, pronto. They hadn't formally lost it - especially since the Saudis were still professing to be loyal vassals.
The Young Turk regime is often mistaken to have been engaged in a "Turkification" program. This is not the case. Their ideology was Ottomanism, which entailed a centralization drive that increased emphasis on the state language - this was not a program to attempt to culturally assimilate the Arabic parts of the empire; that idea was totally alien to their mindset. They would have viewed Ottoman as the state language; its promotion had no ethnic connotations.
The CUP government gained ascendancy because of the crushing loss of the Balkan Wars, which discredited for a time the "liberal" opposition, and they were able to hold onto power because of the war. There was a great deal of resistance to their centralist model in favor of more local control, and I think they would almost certainly have lost power if not for the war.
For the long term, you'd probably see the Ottomans as a fairly significant power. I don't think you can look at it through the European nation-state lens. Iran, for example, is as Persian as the Ottoman Empire was Turkish - in other words, the Turks were the largest ethnic group, but the empire was not constructed to benefit them above anyone else. I don't think there's any particular impediment to it lasting indefinitely.
As for Arab identity, it didn't exist. People identified as Muslims first, and then by locality, i.e. Damascene, Palestinian, etc. "Arab" referred to stinky, flea-bitten desert-dwelling nomads, and nobody would have appreciated being called that, much like "Turk" meant Anatolian country bumpkin. Calling someone from Istanbul a Turk would be like calling a Milanese aristocrat a Sicilian.