I can help you with this. This clicking is a regular complaint on this model that is extremely common... all Diamantes experience this sooner or later. It is not going to be related to the AC operation or whether it needs a charge.
The problem is due to the electric motors that operate the doors inside the AC unit. All three of the doors do a self-test at start up where they move slightly and the position sensor tells the computer where they are. If the position sensor does not match what the computer expects after that movement, it keeps trying to move the door. When there is a failure causing the door position to not match, it is due to the gears in the door motor stripping out... so when it keeps trying to readjust and failing, you will hear the gear clicking as it strips trying to move.
There is a real easy way to determine which door motor is at fault. Start the car up and wait for the click to stop. Once it does, adjust the temperature from one extreme to the other... if the clicking starts again, the blend motor is at fault. If it does not, adjust the mode from floor to defrost and if it starts clicking again the mode motor is at fault. If it does not, switch the intake from fresh air to recirculate (the most common one to fail) and if it starts clicking then the recirc motor is at fault. It will be one of the three.
If you are not wanting to spend a lot of money on this car, you will not want to address this issue. These motors run in the $400 and up range each and installation starts around 2 hours in labor depending on which one is at fault.
The only connection you would see to the AC not working would be if the blend motor was stuck in the "hot" range... this can be easily verified by grabbing the low side pressure pipe under the hood (The larger of the two aluminum AC pipes) while the AC is on. If the line is very cold, then it is possible the blend door motor is stuck in a hot air position. Otherwise there will be a problem with the actual cooling system side of the AC.
When discussing that... if we take for fact the statement you were told about the system not needing a charge...you are going to be expecting most commonly a faulty AC clutch/compressor (no activity under the hood when the AC is turned on) or a blockage in the system (rare, but possible especially if someone has been adding "top up" cans over the years etc).
In any scenario where you are taling about an issue with the cooling portion of the AC (compressor, lines, etc), this particular vehicle is quite expensive to work on.... so if you are on the fence about investing in it, this could be a deal breaker very easily.