Yes it can. As the thrust vector of the propeller is in the vertical plane relative to the body of the aircraft, failure to lock the boom in place would not have a significant impact on safety during the period the motor on the unlocked boom was subjected to climb power settings.
However, during periods where power settings were reduced for the purposes of descent or hover it would be possible for the unlocked boom to sag relative to the position of the locked booms, which could/would induce significant instability problems.
So the answer to your question is multifaceted; yes it could fly but it would not be a safe way to do so.
Just for general info applicable to anyone reading this thread, performing a preflight inspection and assuring an aircraft is safe to fly is 100% the responsibility of the pilot in command. Any failure in assuring the aircraft is correctly set up and safe to fly is 100% the fault of the PIC, whether they understood how to set up the aircraft or not.
Good point, safety first, anything out of the ordinary = no flying.