For the record: The FP3 (that Fairphone has lent me) will boot with all four small modules unscrewed (top, camera, bottom and speaker) and taken out of the device. Please note: The FP3 refused to boot with both all four modules and all screws removed. It only booted again once I had screwed the 12 Phillips #00 screws (there will be 13 in the commercially available FP3) back into the outside of the core module. UPDATE: Actually I think it does indeed boot with the screws not back in – but the display stayed black.
Side note: It took me exactly 12 minutes for one full disassembly. The most time gets lost on 3-4 stubborn screws in the first step of disassembly – I recommend to have a thin needle or thin tweezers at hand to help with lifting the unscrewed screws out. It’s not about force, it’s just that some of the screws will eventually sit/rest in an angle at the outer end of the screw thread (after you have already fully unscrewed them) and won’t just fall out even if you hold the screw side to the ground. Gently knocking on the display doesn’t seem to help much; my vague impression is that you better gently knock at the slim side of the device to help the unscrewed screws falling out.
Be a bit more careful with screwing the top left screw of the bottom module back into place. This screw holds both the bottom module and the speaker module (not alone, but this is the only screw in the device that penetrates two modules at its fringes at the same time). The screw sits in quite a fragile standout hole that looks like it could easily tear open. When you screw these two modules back into their places, bear in mind that this screw must only be screwed back into place once the speaker module is already in its place and once you are screwing the bottom module back afterwards.