I notice very much the cob taste. I notice too the stuff they put on cobs--the varnish or whatever it is, the glue, the paste they use sometimes to fill up the hole in the bottom...
And i find that it takes a looooong time for a cob to start tasting "right"--many months of regular smoking. And I have one cob--a morgan, raw or unfinished--that never tastes right. It always gives an acidic twang to the smoke, also a "raw" taste, especially for the first part of the bowl. I keep smoking it, hoping it will improve, but it seems to absorb the tars slower than my other cobs have. I may just give up on it, which would be a shame, I've already "invested" so many smokes in it, hoping to get it right.
For me, the best cobs are the ones I have smoked until they turn deep gold color, and have a nice layer of cake. I think they taste best when I give 'em a good rest between smokes, too. This is to say, they seem to taste best about the time they become as much tobacco residue as cob, wood, and glue. My old cobs actually seem heavier, from saturation, than the new, though i have not put them on a scale to compare.