Hii

Yes a delhi student can get hostel at AIIMS Delhi. It is generally suggested that you stay at the hostel itself because to study MBBS a lot of effort is required so being at hostel in the campus itself will provide you more options to be focused at your goal. You can reach up to your seniors, teachers  anytime if you require them. You get to usee the library facility, laboratory facility etc. 
So generally it is better that you stay at hostel itself and go home on weekends and holidays.

Thanks!