When your ICX is running switching mode, it's just a plug-and-play hub. By default, all the ports will belong to the same VLAN and no other functions will be performed, other than just switching the traffic between the users and your provider's router.
If you would like the ICX to run as Router, that will require a deeper understanding of the configuration of your provider's router, as the DHCP, DNS, NAT, and Routing functions are programmed by default in the provider's router, this needs to be disabled before you enable it in the ICX.
The ICX in router mode will need a default route to be configured so you can tell the device where to send all the traffic that goes out to the Internet. But it doesn't come with NAT capabilities, so the provider will still need to do the job. Basically, you would need to point all the traffic towards the provider's router as the next hop, while the ICX works as DHCP server and default gateway for your home router.
I'm happy to receiving your feedback. Please let me know if this clarifies your concerns.