I only have an undergrad in biochem with a few semesters of immunology/virology under my belt, so this is my uneducated understanding.
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.
When people are looking, the tiny brushes come out. When nobody's looking, it's shovels and excavators. The quicker you dig, the more artifacts you can find, and the more papers you can write and publish, leading to fame and fortune.
