As an ignorant layperson, I kind of assume we could. A virtual machine thinks it has a network card and a hard disk and whatever, but it's just being given what it expects to see.
The problem I was imagining is that right now we're not recording that data in the way that we're, e.g. scanning the brain's neuron connections. So even if we could rebuild/emulated Frozen Jim's Brain, there may be permanent loss of essential information that was distributed around his lymph system or population of gut bacteria such that 'the same person' cannot be reconstructed.
