Shinki memories are repressed, not actually absent, so it is possible for them to dream things about their life. However, in the event that they do so, they will not remember any details about the dream when they wake up.

For instance, Hokuto might dream about cooking with Seishiro and Subaru, but when she woke up she'd remember something like "I had a dream that I was making cookies. There were a couple of other people there, but I can't remember who."

Other characters who wander into shinki dreams can remember details, but would experience a sense of overwhelming dread at the thought of mentioning any of those details to the shinki in question (the same sort of sensation that gods have at the thought of mentioning a shinki's past to them.)