Feline herpesvirus is caused by infection with feline herpesvirus type 1, which is species-specific and is not usually transmitted to dogs. The virus that causes feline panleukopenia is feline parvovirus (FPLV) and the virus that causes canine distemper is canine parvovirus (CPV). Although feline and canine parvoviruses belong to the same class of parvoviruses, both parvoviruses initially had strict hosts.
That is, feline parvovirus infects only felines, while canine parvovirus (cpv) only infects canines. However, after the continuous mutation of the virus, CPV-2a, which split after 1980, can infect dogs and cats at the same time. Means canine parvovirus can infect cats, but feline panleukopenia does not infect dogs.
To sum up, viral infection in cats does not affect the health of dogs.