[Nitpick]Saudi Arabia didn't exist at the time of World War I; the area was split between a couple tribal states and Ottoman territory.[/nitpick] That said, the Ottomans could certainly decide to take the opportunity to squish the Saud family and any other troublesome groups in the area.
The Ottomans would definately derive some benefits from holding to neutrality; they could throw out the Capitulations and other unfavorable agreements with Europe and would certainly benefit from being able to trade with all sides of the conflict. Britain's blockade of Germany will be somewhat less effective since the Ottomans would be able to trade overland with Germany and serve as middlemen for others wishing to do so.
One thing I'm curious about; what would the status of the Straits be for a neutral Ottoman Empire? Would they allow the Entente to send military aid, supplies and possibly reinforcements to Russia via the Black Sea, or would there be some restrictions?
Assuming a Russian revolution/civil war much like OTL, the Ottomans would be in a difficult position when if they wanted to sieze the Caucasus. While they could certainly take the area (and probably also cause all kinds of trouble stirring up pan-turkist sentiments in Central Asia) eventually the civil war would come to an end and whichever party ruled Russia would demand the return of their territory.
Assuming no calamity, the Ottomans would soon be in a position to make money hand over fist with oil, which if they manage it right would easily be enough to restore them to Great Power status.