Unless it's a product that has the shutter, I doubt it would try to activate it ( it's possible it may sense if the coil is connected), as it needs to know if there is a shutter, otherwise it would try to cal from an image that was not "flat"
Definitely.
That is why I think each product is tailored with it's own (likely non-upgradable) Lepton firmware.
And I expect the ones you can buy OEM will be different again.
Possibly, but if the only configurable option is shutter or not then they could detect its presence automatically by whether or not a coil was connected.
Another possibility is simply that they hadn't finished the full OEM firmware in time for production of F1 and TG165.
I don't think there is enough additional functionality in the OEM version to be worth the hassle of dealing with multiple firmware versions to prevent people using harvested "consumer" units.
Except of course for frame rate - If a >9fps version exists then it needs to be different due to export controls.