Will the cold break throw off the accuracy of the hydrometer reading?
I guess I would hardly call it "throwing off" but yes, anything which is suspended in the wort will change the specific gravity. I brewed yesterday so I have some wort which is just starting to go so there is lots of yeast and some cold trub in suspension. Right out of the fermenter the specific gravity of this beer measured 1.053140. Twenty minutes later it measured 1.053058. A centrifuged sample (clear and bright) measured 1.053037. So yes, failure to remove trub and yeast can throw you off 1 digit in the fourth decimal place. Note that the reason for the decline in SG in the first case was trub settling out over this time period and I could see that. This effect is seen in the fifth decimal place. Removing the yeast had a larger effect. Note that the amount of change induced by removing both is about the amount of error induced by failure to account for the amount of air displaced by the stem of the hydrometer (difference between apparent and true specific gravity).
Suspended material displaced by the bulb of the hydrometer affects the reading. If the material stays in suspension in the hydrometer jar then it is of the same density as the wort, will stay in suspension for ever and thus have no effect on the reading. If this material is denser than the liquid it would have an effect on the reading if it stayed in suspension but it wouldn't; it would settle out. Once it has settled it no longer has an effect (unless some of it settles on the shoulder of the hydrometer). So if you are worried about 1 count in the forth decimal place, let the sample sit in the sample jar for a few minutes before inserting the hydrometer. Practically speaking, don't worry about this!
Obviously I didn't use a hydrometer to measure these samples but I did use a hydrometer for a check reading. I got 13.1 Plato using a narrow range hydrometer which has calibration marks separated by 0.1 Â°P and which, with great care I can read to 0.05 Â°P. The specific gravities given above correspond to 13.129 Â°P for the fresh sample and 13.121 Â°P for the centrifuged sample. Thus the change from suspended trub and yeast is, at least in the beer I'm working on at the moment, less than can be detected on even a high quality hydrometer.