I am currently enrolled in B.Tech at an NIT is it okay for me to do the ISI Kolkata B.Stat program? Consider the fact that I dropped one year after year 12 for NIT.

The path you want to get into is a very dangerous one and it can totally spoil your career without you being able to do anything for it. 

ISI, B.Stat is a very famous course and is known for the entrance paper which is considered very tough by all those appearing in it. The course is tough because the student who is above the cutoff receives a huge financial help from the government covering the major portion of the tuition fee. Apart from this after the entrance exam the candidate can be certain of a well paid job one he/she completes the course and is awarded with the degree.

It gets difficult for the selections if there’s a year gap as lower age students are preferred and in your case there's a two year gap so the chances reduce even more. It would be very risky to change your college again and could cost some harm in your career.