Yes; actually the process was not so difficult in the end.

We skipped the Airtel kiosk at the airport. The next day, we went to a real Airtel store (the one nearest Aerocity). We gave over our passports (with the visa details inside), and in about half-an-hour we had a SIM card each (no cost).

However, they cannot load the 1month pre-pay plan! There is basically one option for INR 378, which gives about 2 GB a day, no issues. The store suggested we go to various nearby shops to get the top-up. This wasn't useful; one person told us INR 500, we didn't find any others. What you want to do is to ask one of the staff to top you up using Airtel Friend; and then pay the them cash. Eventually (after we returned for the 3rd time), one of the staff did this for us (we did not know you could do it, so now you do).

It was easier than expected given all the reports of hassle you can easily find on the internet.

Good luck!