Hi Abhishek,Yes September is a good time to visit Andaman. Season ideally begins at the end of September. Attached with my comments below are packages offered by Tripoto for hassle free traveling. Please take a look, fill the form and someone will get in touch with you. Thanks!
Andaman is great throughout the year. September is an off season and you can expect rains but that shouldn't stop you from enjoying the beach paradise. I was there in June end & I had a great time. The best part is there will hardly be any tourists do most of the beaches will be empty. This should help you plan the trip. https://www.soulandfuel.com/post/explore-andaman-in-5-days Have a great time.
The area receives minimum fluctuations in the temperature and is always pleasant. The best time to visit Andaman Nicobar Island is considered from November to May. Monsoons are however recommended to be avoided for Andaman Nicobar tour because of the high tidal waves, incessant rains and strong winds.