If the surviving Ottomans don't implode owing to issues of inept governance and an oil-centred economy, I might be able to see them making it to 1939.
However, they'll get chewed up by the Wehrmacht in no time, with Anatolia providing a useful bridge to the South Caucasus in 1941. Even if a part of the empire survives in the Middle East, they won't do much.
There's no way that the Wehrmacht attacks the Ottomans in 1941. Attacking Turkey in 1941 OTL would have been a fatal mistake for Hitler, let alone a unified Ottoman empire. That's another couple hundred miles of mountainous, hostile territory across a vulnerable strait passage. And when do you do it? Before Barbarossa, thus making a clear move to encircle the USSR that even Stalin can't ignore? You'd lose strategic surprise and the war gets much harder much quicker for Germany. After Barbarossa? Where on the Eastern Front do you strip armies from? How long will they be out of action, and how will you deal with British troops and supplies pouring in?
A unified and surviving Ottoman empire exponentially worsens this proposal. They'd have had years of war by the colonial powers to profit, renegotiate the unequal treaties, and retool their economies. Then, 20 years of oil profits from an increasingly oil-hungry world to further enrich, arm, and industrialize their country. Unless they go utterly without improvement or reform for all those decades, this is not going to be a house of cards you can just push over-it would be a massive engagement which would be undercut at every turn by the British.
Even assuming they somehow stole a march and charged across Anatolia, the empire is more than that. Try to thrust at the Caucuses across that area, you're going to be constantly at threat of being cut off and encircled by British and Ottoman troops swarming the peninsula.