Not necessarily. The uncertainty principle is a direct consequence of some quantities being "the Fourier transform" of each other. You can't play a pure tone unless it extends infinitely in time, and vice versa: You can't play an infinitesimally short sound unless you ring all frequencies. That's all.
And actually, if something discrete lies at the bottom of spacetime, the uncertainty principle implies that there's a maximum energy and a maximum momentum. For the same reason that there's a Nyquist frequency when sampling. So, if anything, our intuition that there aren't such maxima makes the uncertainty principle hint that there's nothing discrete underneath.
