Do you need to clean no-clean flux?

No, not if your concern is only reliability problems from ionic contamination. No-clean flux contains minimal ionic material that is fully consumed when the flux is activated, or in other words, brought to soldering temperature. If all of the flux isn’t activated, like when you apply a lot of flux but only solder a small area, you still need to clean the PCB.

If you are applying conformal coating, you should remove all flux residues, regardless of the type of flux. Most people understand that when painting something, the surface must be prepared so it is absolutely clean. Otherwise, the paint will quickly lift off the surface and peel off. The same logic applies to conformal coating, even when the contamination is from no-clean flux.