Can a sous-vide circulator fully replace a crockpot?
Would this accurately simulate a crockpot?


No.  Most crockpots operate on the principle of having a relatively low-powered heating element that very slowly raises the temperature of food over several hours.  In many slow-cooking dishes, that additional time spent at lower temperatures is useful in breaking things down, allowing enzymes to work (before they are destroyed at higher temperatures), allowing flavors to marry, etc.  Partly for this reason, most crockpots also have a heavy-duty ceramic insert that does not transmit heat quickly.  Some dishes for crockpots even depend on this -- placing ingredients closer to the bottom which need more time at higher temp to cook properly, while having ingredients that need less high-temp cooking time on top.

A typical pot placed inside a vat of water with a circulator will absorb the heat from the water much more quickly.  The duration of the "transient" (i.e., the time it takes the water to warm up, and then the food inside the pot to warm with it, until they reach a constant temperature) will vary a lot depending on temperature, comparative sizes of the pot and water, etc.

But in general, I'd say it's likely the sous vide circulator will get the water up to a high temperature much quicker than a crockpot typically would.  And depending on the material of the pot, the pot could then transfer heat to the food much more quickly than a typical crockpot would.

Whether this difference is relevant to a particular application or not depends on the situation.  In general, the common replacement for a slow cooker is usually a low oven, as that can transfer heat relatively slowly and gradually heat up a dish like a typical crockpot.  Sous vide is designed to usually raise the temperature of the food to a target as quickly as possible (hence the water bath -- the water transfers heat much more efficiently and quickly than air in an oven or a coil or whatever element under a ceramic crockpot) and then maintain it there.  

In sum: crockpot goal = long transient duration; sous vide goal = transient duration usually as short as possible.