What I have done is to modify the code from here, so I can plot graphs of acceleration, velocity and position. As I thought, nowhere near accurate enough for navigation - although talking to Simon before a meeting this morning, it seems they aren't going to be expected to fly the airship around, just take off, hover and land.
Here's a graph showing what happens when I lift the wiimote off the desk and put it down again, fairly quickly.
The top graph shows acceleration, the middle one velocity, and the bottom one position. I think the best you can say about this is that it's clear that the blue line is the vertical acceleration, and the wiimote started moving about 1.75 seconds after I hit the record button. Calculation errors eventually lead to a bogus velocity in all three directions, even when the device is returned to the rest position - all three velocity lines and the position line should return to zero after about 2.5 seconds.