If it has not completely finished fermenting, then yes, it will, albeit slowly. The temperature has to be "not super cold" however.
I know this because I recently put a kegged lager in the relative cold (40ºF) before it was completely attenuated. It had been a pressure fermentation, and I thought for some reason that the yeast had given up, as FG was stable over a couple of days. I was wrong!
Over a period of one month, the beer absolutely continued to ferment, resulting in excessive foam when poured and some reluctance to clear. Once it was finally finished, the beer cleared perfectly and the carbonation evened out. The flavor also became stunningly clean, whereas before it had some flavors which I wrongly attributed to the malt but which in hindsight were clearly yeast-derived.
Now, if you drop the temp below where the yeast can be viable, I assume this would not occur. It's temperature dependent. So maybe my answer/experience does not apply to you.