I guarantee your ISP’s router has some sort of Network Access Control (either Certificate or MAC addressed) based authentication that controls access to the ISP’s network. The ISP would be crazy to not do that.
It is an easy test. Just by-pass the router and see if it works.
The worse that can happen is your personal devices get denied access.
Yeah the ISP will have to give you an address. The headache might be finding out DHCP server’s hostname. You may be able to find that out from the IP information on the ISP Issued router you have.