Well, they could actually file a case against you if they want to, but what you owe them is probably a fraction of the cost which they'll have to incur in taking legal action. But be warned, it is possible, if they choose to file one court case for ALL of their debtors, then you would be affected. But this is not a criminal offence, so your maximum punishment would be to settle the bill + legal costs, and if you dont then you'll be either faced with a payment plan or sentenced to prison for about 1~5 years.
But, other large subscribers like Dialog, Mobitel, in Sri Lanka, have large scale bad debts, and unlike Airtel, they've got more say in the telecommunication industry, and so far I've never heard nor seen such a case where they sue such a customer, but they definitely blacklist you, in the sense that you are no more welcome to their network.
Airtel is probably doing this to encourage you to make the payment, out of fear.