Luggage or not, irrops or not, the OP may not be allowed to board the first flight without a visa since the final destination is DEL. Sure, everyone has a ticket to leave India at some point, so what? For the ticket being used first, the final destination is DEL. The airline is responsible for checking visa status at boarding.

I suggest calling AI to see if they will connect the two bookings somehow. Don't leave it to the unpredictable decision of the contract employees at the departure airport.