Generally speaking, yes. Of course there are some really high quality 1.8 lenses that are pin sharp wide open, and there are some cheap third party 1.4 lenses that have to stop down to 3.5 before they're sharp. But for the vast majority, I'd say that's the case.
Well, there is no law of optics one way or the other.
However as a general rule of thumb if a lens offers less maximum aperture, the optical design gets simpler.
And if the construction of a lens gets simpler, assuming same standards and tolerances as before, the overall image quality tends to increase.
This is why for example the Nikon 50mm f1.8 are always slightly sharper than the corresponding 50mm f1.4, no matter which version (AI, AI-S, AF, AF-S, ...). Same for the 85mm f1.8 [f2 for AI/AI-S] and 85mm f1.4. Same for the AF-S 70-200mm f4 VR vs the AF-S 70-200mm f2.8 VR2.
Mind, many people accept willingly a slight loss in sharpness if they get the additional possibilities of more light and less depth of field.
And theres exceptions of this rule of thumb. Quite a lot of them, actually. For example for some reason the Zeiss 25mm f2.8 is supposed to be the worst lens of the Zeiss lineup of DSLR lenses, only about average in performance, and inferior to the 25mm f2.0.