IITs should allow it based on: IITs have a direct Ph.D. program themselves, so it would be really bad if they did recognize their own students. Again I am not 100% sure. You can be fully sure by writing to Dean of Faculty Affairs of the particular IIT that you want to apply to.
I don't know about UGC, though.
I like to blog about various topics ranging from education in IITs to social issues in India and US. All opinions and views presented here are my own and not of my employer.