Yes, it is possible. NEET and AIIMS are two different exams conducted in different ways. AIIMS counselling and NEET counselling are two different processes and are independent of each other.

AIIMS counselling is on the basis of marks scored in AIIMS entrance exam. Since the counselling occurs a little later than NEET counselling students tend join a college under NEET. However, If you have secured a seta in AIIMS counselling, you can leave the college you have joined under NEET and join AIIMS.