Ah, sorry. Yes, it will, because a typical accelerometer measures not the acceleration, but the deviation in acceleration from freefall. So it will show an acceleration of 1g when standing on a table, and 0g in freefall.
Which is obviously wrong if you think of it as measuring the acceleration of the laptop. The physical acceleration of the laptop is obviously zero when it is at rest on a table. (Acceleration is the change in speed, and the laptop has zero change in speed.)
Can you build a consistent accelerometer that does what you want?
If you think about the accelerometer as a little micromechanical arm which is being deflected relative to the laptop by the force of gravity, it makes a lot more sense. When they're falling together the deflection is 0.
> Can you build a consistent accelerometer that does what you want?
I gave it some thought, and no, I don't think you can build a self-contained one. But if you allow external communications it becomes very doable (see: GPS system). Also, if you allow another input that tells the device it's orientation wrt. the gravitational field, say a magnetic field sensor, it becomes easy.
If your accelerometer measures what Wikipedia calls "coordinate acceleration" it's something observer relative so I expect (waves hands) "problems" will arise with measuring in relation to your chosen reference frame at relativistic speeds.