I am not so sure the DNA needs to get into the nucleus to be an effective viral agent. Some viruses such as the papilloma virus are able to maintain an episome, similar to a bacterial plasmid, in the cytosol.
The first thing I thought of was "Hey- there is no DNA polymerase in the cytosol, what gives?" And to answer my own question, the virus most likely brings the tools with it to read the DNA anywhere it needs to.
"Episomal latency refers to the use of genetic
episomes during latency. In this type, viral genes are stabilized floating in the
cytoplasm or
nucleus as distinct objects, both as linear or
lariat structures. Episomal latency is more vulnerable to
ribozymes or host foreign gene degradation than provirus latency.
One example is
Herpes Virus family, Herpesviridae, all of which establish latent infection. Herpes virus include
Chicken-pox virus and
Herpes simplex viruses (HSV-1, HSV-2), all of which establish episomal latency in
neurons and leave linear genetic material floating in the cytoplasm"
https://en.wikipedia.org/wiki/Virus_latency
Another:
"all known DNA viruses that infect animal cells encode their own DNA polymerases. In each case, the DNA polymerase is essential for the replication of the virus. Why have these viruses evolved to encode and require their own DNA polymerases? (In this chapter, only DNA polymerases that strictly utilize DNA templates are considered. Information about the reverse transcriptases encoded by retroviruses or the polymerases encoded by hepadnaviruses can be found in Skalka and Goff [1993] and in Seeger and Mason [this volume].) For poxviruses, which replicate in the cytoplasm (Traktman, this volume), the answer may be that the viral genome does not gain access to the cellular polymerases "
http://dnareplication.cshl.edu/content/free/chapters/16_coen.pdf
