Can a discrete sinusoidal signal represent only limited number of frequencies?
It is important to realize that in the discrete-time case, $\omega$ is normalized by the sampling frequency $f_s$:

$$\omega=2\pi f/f_s$$

The inequality in your question is basically the sampling theorem, which says that a discrete-time signal can only represent frequencies lower than half the sampling frequency. All higher frequencies will be folded back into the frequency band $[0,f_s/2]$ (this is called aliasing). If you need higher frequencies then you need to increase the sampling rate.