Cryostorm
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This, Rhomania and Persia need to recover both financially and demographically, not to mention that Persia will need to first bring Central Asia and Afghanistan/Baluchistan into line. Now if that happens and Persia fully focuses on the east, which has a much better rate of return than yet another fight over Syria/Armenia, then they could manage to take and hold the area around the Indus.Back when Iskander The Great conquered northern India in the 1610s/1620s it spurred Vijayanagara to launch an incredibly massive army to drive him out.
As far as I can tell the same Venkata Raya is still the leader of Vijayanagara in 1643. He's still the same guy who considers all of India, not just the southern cone, his sphere of influence. He's still the same guy who in the past has berated European ambassadors for being overly arrogant and aggrandizing. Most importantly, he's still the guy who has far and away the largest army (and a new first-rate navy too, purchased from the Spanish) on the block.
If the Romano-Persians cross into the Punjab or even into Oudh, kill/capture Ibrahim, and then promptly leave, that's one thing. They can probably smooth over any ruffled feathers with a gift or two. If they decide to stick around and set up shop, well, that's something else.
As @Daylight Savings said above, invading India proper anytime soon could trigger the wrath of God.
A big reason for Rhomania to want Persia successful in the east is that this would bring them into direct conflict with China and the Triunes, and Vijayanagara, which is a good thing in Constantinople's eyes. The biggest thing that would need to happen is Rhomania would need to broker a joint border treaty recognition between Rhomania, Georgia, Russia, and Persia for it to work long term.