Can I assume the noise of motion model to be zero? If so, what are the consequences of doing so?
I'm assuming this is with respect to a Kalman filter?
Mathematically, yes it can be zero. The effect of this is that model is assumed to be perfect and estimation uncertainty is due 100% to the uncertainty in the initial state. In the extreme case, if you assume 0 initial uncertainty you will never have any model uncertainty and all your measurements will be ignored.
Even assuming non-zero initial uncertainty the behavior will probably not be what is expected. Consider a simple position+velocity state vector. Over time, the position uncertainty will grow a little bit due to initial velocity uncertainty, but the velocity uncertainty will be constant. No matter how long you wait until the first measurement arrives the velocity estimate will have low uncertainty so not much weight will be given to the measurement.
So, all usage scenarios that I've seen have non-zero dynamic noise.