DoMS IIT Madras - Department of Management Studies Adyar Chennai Answered Questions

Regular candidates should possess a valid score in the Common Admissions Test (CAT) conducted by the Indian Institutes of Management. IIT graduates who obtained a CGPA of 8 and above on 10 are exempted from CAT score. Their shortlisting will be based on a composite score with due weights to applicants CAT score, past academic performance, industry experience and gender.
Sponsored Candidates
This category is of two types: a) Company Sponsored Candidates b) Indian Defense Personnel
a) Candidates may be sponsored by their employers to pursue an MBA at IIT-Madras. Candidates should forward their application through proper channel. They must have a minimum work experience of two years in the sponsoring organization and a valid CAT score.
b) Defense personnel are exempted from the national level entrance test. Candidates who are working with the Defense forces are encouraged to apply through respective government agencies.
Non-Resident Indian and Foreign Nationals
Shortlisting for this category shall be on the basis of
GMAT score
Past academic performance
Letters of reference
Work experience (if any)
They also have to submit copies of their citizenship-related documents obtained from the Indian Embassy of their residing country while applying for the programme.
Minimum Academic Qualifications for Regular/Sponsored/NRI & Foreign Candidates
Graduates (or professional qualification equivalent to that of a university degree recognized by the UGC) in any discipline with first class or 60% marks (55% for SC/ST) earned in their degree from a recognized/reputed University for regular candidates, sponsored candidates, NRI candidates and foreign nationals. For Defence personnel, the minimum percentage of marks in qualifying degree will be 55%. For other categories, relaxation according to GOI norms will apply.
Final year students (of the above-mentioned programme) are also eligible to apply. Such candidates, if selected, will be admitted provisionally, on the condition that they meet all requirements for the qualifying degree before the start of the program and will produce the provisional certificate of completion within two months of joining the program.

Hello Abhinav,
No, you cannot as the candidates should possess a valid score in the Common Admissions Test (CAT) conducted by the Indian Institutes of Management and not MAT scores.
You may refer:
https://doms.iitm.ac.in/index.php/admissions/mba-admissions/eligibility-and-selection
Following are the top MBA colleges accepting MAT scores:
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india-accepting-mat/2-2-0-0-306

You need to secure at least 50 percentile in MAT examination. However, if you have not appeared in either of the competitive examination, you may request the institute to consider you for their Internal Online Examination (IAAT) to qualify for the PGPM + MBA degree programme.

Both degrees have their own values. it all depends from which Institution you get your degree. When we say Institution we also cover university affiliated colleges. Majorly before joining you should focus on counting what emphasis a college/institution is giving on the teaching practices and industry oriented sessions for your knowledge development.