Hello David
You can use CDP to to find information about any directly connected Cisco device, even if they are connected via a routed port or a Layer 2 port. So yes, you can have a switch connected to a router and CDP will show you information about that device, assuming CDP is correctly configured.
Even if you have multiple devices in a network and they are not directly connected to each other, if they are on the same VLAN (like a management VLAN for example) you will see them in the show CDP neighbor output. This is because they are considered directly connected on Layer 2 so they share this information between them.
The only time you won’t see information about the directly connected device is if you are using a QinQ VLAN arrangement, where multiple VLANs are tunnelled through a single VLAN. In this case, you will only see the “neighbors” that are on the tunnelled VLAN and not on the tunnelling VLAN.
For more info about QinQ, take a look at the relevant lesson.
I hope this has been helpful!
Laz