If dust is getting into the HDD, yes. But at that point, the HDD is screwed either way.
So the short answer is: no, it shouldnt. Its likely rattling around on the screws and in the HDD cage when its very active because the head goes back and forth. If you have the know-how, a good idea would be to make some isolation pads and washers. Stick the pads under the HDD if its at the bottom of a cage, so it doesnt rattle around there ( this shouldnt be really needed because most are actually suspended a bit above the cage ) and put the washers in between the HDD and cage at the points where you screw it in.