you can only find it if it's on and if it's connected to the internet
if find my iphone is enabled read
Find your lost iPhone or iPad with Find My - Apple Support
if find my iphone is not enabled then you can't use the link, if the local law enforcements is presented with the IMEI and they get a warrant they can force the carriers in the country to triangular track it with the IMEI (it's usually only used in missing persons cases, doubt law enforcements would spend those amount of expenses on theft )
the serial number serves no purpose in that respect