Yes, the concept of the immortality of the soul (ātman) is explicitly presented as a necessary condition for Rebirth (saṃsāra) in the Bhagavad Gītā. The Gītā's teachings on rebirth fundamentally depend on the soul's eternal and indestructible nature.

In Chapter 2, Lord Krishna explains to Arjuna that the true self (ātman) is distinct from the physical body, which is transient. Verse 13 states: "As the embodied soul continuously passes, in this body, from childhood to youth to old age, the soul similarly passes into another body at death." This passage clearly establishes the ātman as the enduring entity that transmigrates.

Further, verses 20 and 22 reinforce this: "For the soul there is never birth nor death. Nor, having once been, does he ever cease to be. He is unborn, eternal, ever-existing, undying and primeval." And, "As a person puts on new garments, giving up old ones, the soul similarly accepts new material bodies, giving up the old and useless ones."

Without an immortal, unchanging, and indestructible soul that transcends the death of the physical body, the entire mechanism of rebirth, governed by karma, would be nonsensical. It is the eternal persistence of the ātman that allows for the continuity of experience across different lifetimes and the accumulation and working out of karmic impressions. The soul merely changes its physical dwelling, much like shedding old clothes, ensuring the cycle of saṃsāra continues until liberation (mokṣa) is achieved.