Is it metaphysically possible for a disembodied Cartesian soul to so much as form any purportedly empirical beliefs, even if only ones that are false?
Yes it can. That is the idea behind Empirical Idealism, the philosophy of Bishop Berkeley.
The scenario you mentioned is already described by DesCartes in his famous demon example.
Berkeley takes this reasoning a step further: Not only is it possible, but it is true of the world. Because we can only be certain of our own sensations (empirical evidence) and nothing else, the only thing we have real knowledge of is our mind, and non mental objects (i.e.the material world) is but an illusion. Other people are disembodied minds as well, and the world outside of human observation is just images in the mind of God.
On the other hand, a materialist, by definition, argues that a mind cannot exist without a body, since mental states are nothing but a collection of brain states and nerve stimulation.
The question, now that we have a notion of how neurons work is "Where would it put the memories?" I think our understanding of the brain, incongruously pushes us toward Kant, and the idea that any non-physical being would have to be 'eternal'.
Memory is an exothermic chemical process, so anything non-physical should not use it. It would instead have fixed beliefs independent of time. So Kant's God and his angels make sense, but a learning by ghosts does not.
I don't think so:
Consider a soul (or mind) that has always been disembodied. Suppose he has empirical beliefs. Then how can he with any justification call them empirical? Empirical by its very sense means to have reached some conclusion/understanding by reference to the real world, and this through sense perception; do to call them empirical beliefs is incoherent - the most he can justifiably say, is he has beliefs.
But there is a subtlety; say we have a soul that is disembodied now, but for some extended period in the past he was embodied; then he could have conceived some empirical belief - the physical fact of gravity, for instance - and this has remained with him when he 'slipped this mortal coil'.