Doesn't seem possible. You''ll need one of the following as well:
Otherwise you could also try just walking into a store (petrol station, etc.) with your card and asking for a plan.
Could you elaborate on why it is so hard to get a SIM? Here in Europe it couldn't be easier, and most providers give you the SIM for free if you buy a certain amount of airtime.
Many people don't have the required ID to get a SIM. So they used to have someone else buy them a prepaid SIM and then use it under that person's ID. In some cases, they'd do something illegal and finding the right person was painful.
There were many cases in the early days where people would use fake ID and buy postpaid phones. They'd use it as long as the operator would let them, without paying the bill. Rinse repeat the fake id. There were a bunch of folks who did this when we were at university - IIRC, they went through a half dozen handsets in 3 months and ran up large bills. There was an black market of sorts for such mobiles - buy it for Rs.500 (reliance), resell it for Rs.1000 and use it for Rs.10000+. People used to call in to one of these phones. the owner of the phone would then conference them on long-distance (expensive then) calls and international calls 😉
Finally the terrorism thing, where the government said that wanted to avoid giving them an easy way to communicate. they also banned the hiding of one's number in the caller id because people were making too many crank calls and creating trouble.
At the end of it all, the rules mandate official ID proof. Activation needs a background verification to be done. While this does not work in reality, the number of postpaid dine-and-dash type situations have been reduced.