Plank length gravitation.

[Aphex_Twin]

Can two objects move towards each other as a consequence of their gravity a distance smaller than one planck unit of length?

[selfAdjoint]

It's not clear that the idea of position, and hence of "moving toward" has any meaning at the Planck scale. Spacetime may be foamy, uncertain, and/or topologically complex at that scale.

[Fredrik]

No one really knows what "distance smaller than one planck unit of length" means. So the question probably doesn't make sense. We'll have to wait for a better theory to know for sure.