Mostly when one is interested in bokeh, it is the performance of the lens when used wide open which may be most important. There may be exceptions, but usually the aperture blades are completely withdrawn and the shape of he aperture is completely round.
At a very basic level, that is quite true. But it can get much more complex. For example the Nikkor 85mm f/1.4D AF-D lens was designed years ago specifically to have pleasant bokeh, as were the 105mm and 135mm f/2 DC lenses. As opposed to those, other examples of less expensive lenses that are commonly referenced are the old Series E 70-150mm zoom and the 85mm f/1.8D AF-D lens. All of those are commonly compared, and the relatively inexpensive 85mm f/1.8 lens has often been cited as "good enough".
But in fact the 85mm f/1.8 lens is not even close! It has relatively decent bokeh only when shot virtually wide open. Of course it isn't as sharp at f/1.8 as it is at f/4 either, so it's take your choice, sharpness vs smooth bokeh. The manual focus 75-150mm f/3.5 Series E zoom suffers the same problem (and is basically a "cult lens" due to the great bokeh wide open, not to mention the low cost).
But the 85mm f/1.4 lenses and the two DC lenses all have 9 rounded shutter blades, and while DOF changes and the amount a of out of focus changes, the smooth bokeh is retained even when stopped down! Getting the subject sharp does not automatically eliminate smooth bokeh. The creative potential for the lenses with rounded blades is significantly greater than what can be done with the others.
Hence for those with advanced skills and requirements, the difference is quite significant.
Does that then mean that the bokeh under these conditions is always wonderful? Definitely not. That's because it is the optical design in terms of lens elements, refractive indices and curvature which is the biggest influence on whether the bokeh is harsh or pleasing.
I'd put number of aperture blades much lower down the list of important factors.
But virtually every modern lens that is designed specifically for good boken is also necessarily going to have 9 rounded blades in the diaphragm. If the design target did not call for rounded blades, it almost certainly did not consider bokeh at all for other parameters either.
Where aperture blades do play a very important part is in diffraction effects. At smaller apertures, bright point light sources within the image may be rendered as a 'star' with multiple rays radiating outwards from the light source.
Typically, the pattern from an even number of blades will have the same number of points, e.g. six blades gives six points. But an odd number of blades will give double the number of points, e.g. five blades gives ten points.
And more is generally better, if for no other reason than each ray of light from the point is also half the intensity when generated by a odd number of corners. Note also that as has been mentioned even "rounded" blades are not perfectly round, but the more blades the less the imperfection. Hence a diaphragm with only 6 blades, even if they are rounded, will be very poor compared to a 9 bladed diaphragm with rounded blades.
