Definitely go for accredited, there's no sense in spending time in a graduate program without getting accreditation. 

US has some very good grad programs, the best being Harvard GSD, Yale, Berkley. It depends on your finances. 

Non accredited is suicide! I went to a non accredited school and it took me 10 years to overcome the obstacles at NCARB and that was 30 years ago when they thankfully allowed me to use work experience to overcome the deficiency. Hell, today I would guess you probably could never get an NCARB Certificate going this route. If you plan on working in the USA a NCARB Certificate is essential.

Can you pursue Mdes and then get the NCARB certificate? Or do you absolutely need M.Arch?

if you go to NAAB's website they have a list of accredited degrees.  if its not on the list it won't help you become licensed. 

Is your degree acceptable to ncarb? i assume not but worth asking...

Your choice depends on what you plan to do with regards to being an architect in the U.S.  

If you desire to become an architect in the U.S., it may be advantageous to obtain an accredited professional Master of Architecture.  http://www.naab.org

However, if you plan to return to India, it is not necessary to obtain the accredited degree; instead seek the post-professional MS in Architecture - pursue the degree at an institution that specializes in your desired topic.

Regardless of your path, you can always seek licensure in the U.S. with your education evaluated by EESA (check NAAB website). I would think with your BArch and U.S. degree, you would meet the standards.

Although accreditation doesn’t guarantee you job but it is important to pursue your career with accredited universities. It reflects the quality of education of the university you completed your graduation. It is about public trust, therefore it is of high importance for employers.

As a student, it is of high value because it aligns your educational process and improves your knowledge through experienced and qualified faculty members. Overall, the objective of accredited universities is to advance the education with full collaboration of students, faculty members and administration.

Therefore, enrolling in an accredited university is important as the student is engaged in a continuous improvement and skill enhancing process.