Yes! It won’t be an IIQ Rule, but in the Google Devices App, General Settings, you can set criteria for OrgUnitPath Translation Map that would include Owner > Unassigned and any other filters you’d like to have in place.  This should update all of these devices in the overnight sync to move them to the OU you’ve designated in those mapping rules.  Once the mapping is set up you can click Push Data on a device’s Asset Information page and it’ll change the OU right then, not waiting for the overnight sync. 

Just to add onto what @AJennings 2039489 daretolearn wrote (great answer), here’s our documentation to help set up Google OU write-back: