That depends whether you think that you are increasing the probability of a Boltzmann brain coming into existence by a greater factor when you stir your coffee, in comparison to when the memory of the computer is randomized.

I'm sure the coffee contains enough atoms for a Boltzmann brain to form. However, the entropy of the coffee is already high from your point of view before you stir the coffee, i.e. the probability of the coffee containing a Boltzmann brain is changed little by your stirring it.

It also depends to some extent on the size of the computer memory in question. We can infer that it is vast, since it is capable of simulating a human. However, is it just sufficient to do that or much bigger still?