Yes. The connection between HPV and head & neck cancers as well as lung cancers has been established but have studies been done to sequence the genome from these tissues rather than just to find out the presence of the HPV?
I don't think whole genome sequencing is the most efficient route to the answer of that question. The papilloma and polyoma viruses have different mechanisms of transforming cells in cell culture, and likewise would be expected to have different mechanisms of transforming cells in the whole organism. Many times the "trigger" which sets a cell line down the road from normal, to rapidly dividing, to fully metastatic, is not easily detected in the majority of cells in the fully metastatic mass.
Also, knowing a great deal more about how these viruses trigger cancer may help us to fight cancer in general, but reducing deaths from these viruses is far easier to do with vaccines to prevent infections (and perhaps to help our immune system fight virus-induced cancer) than by studying the genomes of metastatic cells.
There are a number of studies who have captured virus and tumour DNA and RNA sequences: http://www.pnas.org/content/111/43/15544.short http://genome.cshlp.org/content/24/2/185.short and https://www.nature.com/articles/nature14129 for example. You could also mine HPV genomes from published cancer genomes and address the question that way, if these papers don't cover the role of viral genome diversity in the way you're thinking of.