Either way would work, though you would certainly receive more data if your configure the node to be monitored via SNMP. The real question is how you have your alerts structured. Even the default "Node Down" alert would function in this case. If you've customized this alert already to be specific to servers, then it would just be a questions of duplicating it and modifying for your Cisco gear.
As Rob stated, you can do both. You can definitely add Cisco devices in and poll them with SNMP. If you have SNMP configured for a device it will be polled via SNMP and ICMP to gather all sorts of great stats and metrics on the device. Here's a Cisco guide on how to configure SNMP on your device(s):
You can also enable the SNMP agent on your windows servers and gather some great data there as well. For your Windows systems you can poll WMI, SNMP, and ICMP.
I'm not sure why you wouldn't want to be notified when a server goes down?
In order to only get an alert on the switch and not on the server, you need to create a dependency to make the server a child of the switch (parent). By creating this dependency, the status of the server goes to UNREACHABLE, while the status of the switch goes to DOWN.
You do this via Manage Dependencies in the admin page.