[sev], idealistically, yes, that would perhaps be the idea -- a door for something -- "a unique chain of memories?" to walk between these mediums? I have to say, having been through general anesthesia once, I had an "Aha Moment" -- thinking -- "So that's what cryonics should ideally feel like! However, I do feel a bit out of phase: it felt instantaneous -- as if I didn't lose any time, although the surgery took more than an hour: what a weird thing, am I still me with this memory discontinuity?" :) So, I think it is probably the closest to perfect, that the future of cryonics should be able to get to.
If the "unique chain of memories" is what defines one's identity, then I could theoretically imagine that another processing unit, like a brain-CPU, could take on a little journey to derive its further actions from that "unique chain of memories" to append new memories based on those new actions, then suspend that, and write new memories back to my biological brain, and let me resume.
To realize this ideal at this level of mind uploading would require that "brain-CPU" be memories-compliant: i.e., allowing itself be controlled by "unique chain of memories" that defines me, and be neutral and unbiased otherwise.
However, what if what defines me to be me is not "unique chain of memories?" -- but rather, a pseudorandom process coded in the totality of components that make up the brain that, even with a very small epsilon of deviation, chaos-theoretically significantly diverges in the actions it produces diverges from the original? (i.e., it is not IIMT-x-equivalent)