In a standard mechanical wristwatch (swiss lever escapement), the escapement error causes the watch to run slower when the amplitude drops. Watch designers (and adjusters) can compensate for this by hairspring design. Ideally, if the compensation is perfect then the watch's rate doesn't vary with amplitude. In the real world the watch may be undercompensated (watch slows down) or overcompensated (watch speeds up). So it depends....
I don't know if the co-axial escapement has a similar escapement error as a swiss lever escapement so your mileage may vary.
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