I guess that depends on the definition. How do you define a cell in the body as human and another cell as not human, when both are necessary for the human as a whole?
by their genomes?
On that note, 'I' am in many ways a 'we'. I am an orchestra, a beautifully complex and rich interchange. As are you.
I would assume not for viruses.
Wet markets make zoonotic diseases more probable since they are an intersection for several disease reservoir populations. Novel viruses have more opportunity to jump species since the animals are often sourced from diverse wild populations, and many animals and humans are present together.
A septic system is used predominantly by one species - humans - that are already in close contact. They may aid the fecal-oral transmission route for an existing disease or be a breeding ground for bacteria, but I wouldn't expect novel viruses to arise here.
Edit : I might have misread the intent of your question. I wouldn't have expected these sources to generate novel viral diseases in the time in which they were used.
If you're wondering whether they sequester diseases that have been forgotten by the immune systems of people alive today, that seems quite possible. We're finding all sorts of interesting things in peat bogs and permafrost. If this environment adequately preserves bacteria or viruses, we might find something. I honestly have no idea about this kind of preservation, though.
Part of that I suspect is an (unofficial) tradition of licking archaeological finds for luck...
Sounds like material for the pre-credits sequence of a low-budget horror movie.
I'm quite sure that it wasn't a joke.