I suppose so. I would think that the swirling effect of an active fermentation would keep the temp of the beer fairly uniform from edge to core. But I can see your point when talking about the lag phase or during bulk storage after fermentation has subsided.
Yes, there will be some mixing as a result of the active fermention and convection currents, but there will be some lag in the response time regardless.
If I go this route, should I be insulating the part of the probe that is exposed to the ambient temperature? Otherwise, it seems like my probe would get confused about which temp its supposed to be reading, the 68 degree beer, or the 62 degree air under my stairs.
Any suggestions as to what works best?
Yes, the insulation would help and especially so if the ambient temperature is substantially cooler than the target temp. You can use just about anything for the insulation. Something like the bubble foil insulation would be ideal, but just a piece of foam rubber or even a doubled over wash cloth would work. IOW, anything to trap the heat radiating from the fermenter.
So long as you are not fighting extreme cold, I would think that you could easily maintain the fermenter temp within one degree of your target with the differential set tight at 1 deg or so. Be sure to set the Anti Short Cycle delay to zero so that it does not over ride your differential setting. ie, if your diff is set at 1 deg and the Asd feature is set to 2 minutes, the heater won't be energized at less than the 2 minutes. I don't remember if the controller will even allow you to do that, so it may not matter, but something to check anyway. If you are working against extreme cold, you could throw a blanket or sleeping bag over the whole thing for added insulation or maybe build an insulated box of some kind.
Thanks for your help so far and in advance!