Well yes of course it would, but HOW LONG would it take to get into full swing?
The conflict I was for seeing was over the rest of the Arabian penensula, as the UK was already incroaching there.
This is a difficult question. The Entente victory led to a reorganization of the oil company granted a concession to remove German interests in favor of American and to a lesser extent French and British interests.
Also, the British interests involved saw Mesopotamia as a "strategic reserve" for their already-developed fields in Persia.
In general, though, the war gave the Ottomans a much stronger hand than they had had previously, so they might very well have forced the issue by threatening to cancel concessions.
Regarding Arabia, the Saudis had evicted the Ottomans from the Hasa (the oil-rich coast of the Persian Gulf), but if not for entering the war, the Ottomans would have certainly and easily regained this area, and probably worked to consolidate greater control over the interior as well.
So, when Arabian oil is discovered, it's going to be Ottoman.
I think in a case where the Ottomans stay out, even Kuwait is an open issue. If the war is dragging on, restoration of full sovereignty by the Ottomans might seem like a very small price to pay for a friendly empire.
There is very little benefit to Britain to see Arabia detached from the empire, as it's a lot easier to deal with one government than several, especially one that they have influence with as opposed to a fairly unpredictable Saudi regime, and direct control over the area is a huge waste of resources for an already wobbly empire.