I was thinking of the accelerometer being located near the outside of the shell, rather than relatively stationary near the centre of rotation. I agree it's not entirely trivial, but it seems pretty doable to me.
The accelerometer cannot measure the earths gravity which was probably what the GP suggested. However you can measure the centrifugal force (http://xkcd.com/123/) which may be more precise than trying to measure the muzzle velocity or just assuming certain known muzzle velocity.
Maybe there's still some minuscule effect that can be detected, though. The sections on Magnus force in http://www.nennstiel-ruprecht.de/bullfly/index.htm seem to suggest that this is the case. But now I'm not so sure it's as simple as counting the number of periods of oscillation from the accelerometer.
IANAIBOEP (I am not an expert in ballistics or even physics)