No, the MCU2 upgrade is independent of the AP3 upgrade. Since you already pre-paid for FSD, you will get AP3 computer for 'free'.
MCU1 supports AP3 so you do not need to upgrade your MCU. There a multiple threads (in addition to the URL posted upthread) that detail what additional functionality you get with MCU2. If you choose to upgrade, the cost is $2,500.
Also, if you are interested, read through the FSD blog posted by Tesla -->
Full Self-Driving Computer Installations