Can a component with no history with an EASA Form 1 marked Inspected/Tested be installed on an aircraft?

Yes, provided that it has continued to apply the requirements of point 2.8 of AMC 2 of 145.A.50(d) to re-incorporate the component into the EASA system. 
It is not required to ask for more documentation than the Form 1 to the CAMO that orders its installation. In case of doubts about this component, it would be necessary to go to the P145 in question if we are the competent authority (or notify the corresponding authority) to assess whether they have done everything necessary to put the component in the system. But without penalizing CAMO during this process, that is, independently.  
If during this investigation in P145 it is discovered that there have indeed been irregularities with the component, the CAMO will have to be notified and the component will have to be dismantled.