Would Ottoman neutrality be enough to save Russia?

Would the Ottoman Empire staying out of the Central Powers be enough to keep Imperial Russia in the war?

Not reliably, because Ottoman strategic interests still opposed Russian control of Constantinople and access through the Dardanelles.

The Ottoman government cannot treat Russia as an ordinary neutral neighbor. Russian pressure on Constantinople and the Dardanelles is a long-standing strategic threat, reflected in the orientation of the straits' defenses. Religious claims about protecting Orthodox sites reinforce, but do not replace, the practical Russian desire for warm-water access and control of the Black Sea gateway. Even an Ottoman Empire outside the Central Powers would therefore have strong reasons to obstruct a more powerful Russia. A viable rescue still needs an operation that opens the route rather than passive Ottoman goodwill.