It is very doable but the cost and learning curve may be an issue.
You would need loading and unloading fixtures as well as some sort of PLC interface.
We have around 1000 robots on a 3 shift operation. Something as simple as a part present switch stops production until someone intervenes. Sounds like you want it to run in full auto pilot at night, You would more then likely come in in the morning with one or two parts complete and the system halted for some miner issue.
I don't know how big these parts are, but I would consider making a well built rotary table and mount 3 or 4 parts at a time on the table. Use it as a forth axis or use a PLC and drive to interface with the
CNC.
Good luck