From what I read, the Russians had to evacuate Crimea even before the Habsburgs called it quits because of the outbreak of diseases among the soldiers. Could the Russians really expect to gain more from this war compared to OTL? On another note, without the embarassing defeat of the Habsburgs ITTL, would Frederick II still feel confident enough to invade Silesia?
The Russians invaded the Crimea twice: in 1736 under Munnich (and evacuated it due to the plague) and in 1737 under Lacy (and evacuated it in 1738 due to the supply shortages). But in 1737 the Russians took Ochakov (which they had to evacuate the next year due to the plague) and in 1739 Munnich advanced into Moldavia, defeated the Ottomans at Stavuchani, occupied the fortress of
Khotin (August 19) and
Iaşi. In parallel, the second Russian army invaded Kuban.
These successes had been offset by the Austrian defeat and separate peace. As a result, Russia got only Azov (on condition that it will not be fortified), some small pieces of land on the Dnieper and declaration of Kabarda as a neutral buffer state. Russia was not permitted to have a navy on the Azov and Black Seas and all naval trade had to be carried by the Turkish ships.
So, without the Austrian defeat, Russia definitely could get the better conditions. An access to the Black Sea coast and permission to create a Black Sea fleet would be quite realistic in exchange for returning Moldavia.
Annexation of the Crimea was not of a vital importance (CII a vassal state for years). The important thing was to demonstrate that the Khanate is not anymore invulnerable to the Russian attacks. This was a fundamental change of the existing perception which made the Crimean raids very risky: between 1711 and 1739 the raids had been happening practically annually. Then there were
Crimean raids only in 1756, 1763 (during the 7YW) and 1769 (during the Ottoman War of
1768–1774). Without a major distraction of the Russian army the Khanate did not risk the raids anymore. After the battles of Lagra and Kagul in 1770 the Crimeans almost ceased to bt the military factor: in 1771 it took less than 3 months to achieve capitulation of the Khanate.