No!
I say that manual gearboxes without any hydraulic actuators and pumps (wheels half immersed) are suited for mineral oil like 75w90 ...
A. GM and Ford specified ATF for their Borg-Warner T5s.
B. These transmissions have a good reputation for quality.
Can you not conceive of something a little different than what you've seen? You say the transmissions which use ATF to good effect are designed different. So maybe the T5 is designed different, because of A & B.
What's the point here? If you get a thin film of the stuff on the working surfaces of a bike chain, then it will protect against wear. It may also be somewhat less resistant to being flung off or dripping off than the 75W90, so you may have to reapply a little more frequently.