Yes and No,
Nano-materials could resist nano and larger materials from being caught in it. But might not be able to resist smaller than nano materials from being caught like reactive compounds.
Take for instance that spray you put on objects so water based substances slide right off. How that works is by spraying on silica particles onto the surface of an object. Those particles work on a molecular level (smaller than nano) to repel water based substances. And even then it can be damaged by a scratch or bond with some other compound.
Alot of this depends on the structure, chemistry, and end composition of the nano-fiber. For instance spider silk is a nano-fiber based substance formed from woven protein chains. Stuff gets caught in that all the time.
What really matters here is what is your definition of clean?