Earlier quoted context omitted.
No. An accelerometer measures change in acceleration. When the round is fired, it will experience a huge acceleration from the propellant along its axis plus a very large rotational acceleration as the rifling spins the round from 0 revolutions per second to a large number of revolutions per second. Once the round leaves the barrel, it is falling at a constant acceleration (9.8m/s, freefall, 0G, "weightlessness"), so…
I got it wrong in my first sentence - in order for an accelerometer to be used, there has to be changes in acceleration proportional to distance travelled. Per the rest of the discussion, there isn't any.
Users usually calibrate the device at rest to get a good estimate of G so that it can be subtracted from accelerations measured later. Is that what you mean?