If I am reading the datasheet correctly, it wouldnt be able to detect a turning of the wheelchair. It would only detect a tipping of the wheelchair forward, back, or to one of the sides. The diagram labeled 'rate sensitive axis' describes this. THe only way this would really work is to put a gyro sensor on both wheels, which would be a problem..
If I am not mistaken, one wheel moves more than the other during a turn. As chagrin said, a sensor watching the spokes of the wheel would suffice. Speed can be measured in spokes/second or whatever other time constant is convenient. When one wheel's SPM is (x amount) higher than the other's, a turn is occurring. the X amount can be changed to accommodate wheels with different amounts of spokes and other variables.
That would leave you with the issue of distinguishing forward from backward.