(The response below is from 2015 U.S. Bose Scholar Daniel Howard who did his internship at TIFR in Bangalore, India. Although many of details apply to Bangalore, much of the information provided can apply to any campus/city in India. Thanks to Daniel for his detailed response!)
“Not the answer you’ll like but probably not. My experience was that it’s only possible to set up an Indian SIM in India. But here’s some advice.
For doing this at NCBS near Yelehanka, your closest shop that has that capability is the below address. Other Airtel stores nearby can’t process new SIM government forms when I tried them.
No 8, Jammathi Shopping Complex, BB Road, Opp Post Office, Yelahanka, Gandhi Nagar, Yelahanka, Bengaluru, Karnataka 560064, India
You need to bring two passport size photos (which can be cheaply made at many stores around India as you’ll need more for other things in country). Also, encourage a friend to go with you to help fill out the form. Plus you’ll need to provide them with a friend’s cell number which they can text/call to verify your new line and other things. It can take a week or more to activate, especially if a form is done wrong (which I learned from experience).
Alternatively, I know another U.S. Bose Scholar who was at NCBS (in Bangalore) and she made some friends/met colleagues the first few days who had extra basic phones with SIMs to give. WiFi at NCBS is also compatible with eduRoam so you can login immediately using most US college credentials and contact others via WhatsApp, Google Voice, or other internet services on wifi. Colleen at NCBS can be a big help too.
Once you have your own SIM (assuming you choose Airtel which is what I had) you can add money to the line at any Airtel shop, like the small stand on IISc’s campus. I recommend depositing about 500 INR then using *121# (no internet needed) or the Airtel app (needs 3G/internet) to redeem bundles you’d like. That 500 last me two months paying per minute/SMS charges and getting two one month 3G packs.
If I remember correctly, dialing *121# then selecting option 5 which appears gives you deals for your line that will give you the cheapest possible rates I found for minutes and 3G/4G services, even better than the app’s or store’s rates. I believe you can activate 3G through the *121# menu but I may be mistaken and you should do that at the stand once money is deposited so the clerk can help if issues come up.
Hope you enjoy India and wish I could go back with you!”