Not quite. The exclusion zone is pretty touristy, and there are always people there working. The dogs are mostly tame and friendly, and they happily engage and socialise with tourists.
One thing to understand about Ukraine is that many animals are kind of like community pets. They don’t belong to anyone in particular, but they live in one area and are fed and cared for by all the people in the area. People (and even businesses!) build small shelters for the animals. The Silpo supermarket downstairs from the last apartment I lived in had its own little cat shelter fit for about six cats, and painted nicely with Silpo branding.