A device (serial number) can only exist in one org. If you attempt to claim a device serial into the network which you don't have in the org inventory, you'll receive an error:
{ "errors": [ "Device with serial Q234-ABCD-0001 not found" ] }
If you attempt to claim a serial already in the network:
{ "errors": [ "Device with serial QXXV-FXXR-XXD7 is already claimed and in Test Network (network ID: L_9906373669455549372)" ] }
Otherwise, success is just a 200, OK; success.
The Meraki Dashboard will not allow you (or your API key) access to inventory that you don't have privileges for.