No you don't have to swap them out to boot the machine. It wont work properly, but will go into attract mode, run the tests and start a game. I was only suggesting this to save a little time if you are poking around testing various components.
Try your display card by itself first, then the MPU. I'd also keep the MPU/Driver boards together, no reason to separate them and risk any damage or wear.
If you do find its the MPU and want to swap the roms, you only need to swap the 2 game roms and not the Flipper roms. The flipper roms are actually the 'OS' for the machine and should be the same version for both of these games. Be very careful with the legs and take a picture to make sure you put them back in the right position.