Is it important to learn any coding language before taking admission in IIIT Delhi, and if not, which programming language would you recommend I start studying just for fun?

Yes, it's advisable to learn a coding language before being admitted to IIIT Delhi although it's not completely necessary. IIIT Delhi organizes some coding sessions during the orientation for people with non-CS backgrounds. If you have no knowledge of coding, you don't have to worry much because many non-CS students have launched successful startups. All you need is the determination to work hard and interest to learn new things. 

If you are adamant about learning a programming language, choose Python. You will be introduced to the world of programming through this and get excellent exposure too.