I spent 3 months camping, fishing & exploring the Andaman Islands when it first opened to tourism over 15 years ago. It was the greatest adventure of my life... total paradise, total hell at times too. I am sure a lot has changed and I doubt they will let you camp everywhere like we did.
I didn't do any tropical fruit specific exploring but did find a few gems -- like a luscious pink-tinged pineapple that I couldn't eat in peace because a hungry village cow was utterly determined to eat it right out of my hands - and it followed me around the whole village, salivating and pestering me. I enjoyed visiting the more remote outer islands like North Andaman and Little Andaman. Some favorite spots were Ross Island near Port Blair, hiking the mountain / highest point on North Andaman, Ross and Smith Island and Diglipur town on North Andaman, the mud volcano on Baratang Island, and Whisper Wave waterfall in the jungle of Little Andaman. I think its worth chartering a boat / fisherman to take you to visit the many beaches and reefs that are inaccesaable by road or public transport.
I would bring my snorkeling gear although I am sure its widely available there to rent now, I would always want to have it on me.
Caution: I was infected with a nasty tropical parasite called Schistosomiasis while wading in fresh water -- where rivers run into oceans / bays. I would personally avoid entering any fresh water or anywhere near snails as I can personally confirm this infection exists in the Andaman ecosystem and you don't want it.