DHCP itself is off limits here, as it's above OSI layer 4, however, this is about the router and its general abilities as it applies to operating as a DHCP server, so that part is allowed.
All Cisco devices that can operate as a DHCP server have conflict checking mechanisms. So, yes, the router would mark the IP address as bad/in-use/conflict. Additionally, you can set intervals (on most devices) to re-verify whether a conflicting address is still a conflict or whether it's safe for it to remove the entry from the conflicts table and assign it to something needing an address. Just remember that if the conflicting device comes back online at some point, the address will be marked as bad again (like if the device was simply turned off for the day).
To avoid this issue you can either change the static IP address to something outside of the scope or create a DHCP reservation (or exclusion) to prevent the DHCP server from trying to assign it.