Soviet carrier politics beyond the Montreux Convention

Without the Montreux Convention, would the Yak-38 still have existed?

Yes. Internal Soviet politics would still obstruct conventional carriers even without the Montreux Convention.

The Yak-38 is still expected to exist in this counterfactual. The Montreux Convention creates an obstacle that Soviet planners have to work around, but internal Soviet politics are treated as the decisive barrier to catapult-equipped carriers. Removing the convention therefore leaves the institutional reasons for choosing a different form of naval aviation intact. A treaty change alone would not settle the carrier argument inside the Soviet system.