Atleast with MTNL you can do that.
Purchase modem yourself and put in the application for new ADSL connection stating you already have modem / router. I kept my router connected with the usual login info ( for mtnl default login is your telephone no and password is C/A no from telephone bill, you can change password afterwards. ) and my connection was activated in matter of 2 days. But those who applied for router + connection had to wait for months.