There would still be fast-moving air in the middle of each pair of fins. Only the air touching the surface of the fins that would slow down, and I think that would be beneficial because it would allow the air touching the fins more time to actually absorb heat. You have a point about dirt reducing heat conductivity, but anodized aluminum has a microscopic honeycomb texture anyway (that's what the colored dye soaks into), so I think some dirt adhesion will be unavoidable; the heatsink will have to be cleaned regularly for best performance, no matter what.

Ultimately the only way to know exactly how those factors would affect this specific design would be to make multiple heatsinks with slightly different surfaces and test each one in identical conditions. Whether it's worth doing all that work for a hobby, I don't know.