They definitely do, which is why oncolytic virotherapy is not as simple as just direct oncolysis of tumor cells. It also relies on the highly immunogenic virus to attract T cells and other lymphocytes that may recognize the tumor to the microenvironment (antigen spreading).

It is also why these two modifications to our virus were chosen, integrins and retinoblastoma dysfunction are vital for a successful cancer cell.

I work and research oncolytic adenoviruses that are used for cancer treatment; the virus our lab uses makes use of two selection characteristics. The first is a modification to the casid "fiber" which only allows infection of cells over expressing integrins, which are associated with many types of tumors. The other mechanism to restrict replication to cancer cells relies on modifications to the virus genome; which in turn only allow for replication in a cell where the retinoblastoma gene is dysfunctional. The adenovirus protein normally binds to retinoblastoma to stop surveillance mechanisms that would push the cell through mitotic stages. If you remove the gene expressing this protein, the adenovirus can only replicate in retinoblastoma deficient cells. Retinoblastoma also is deficient in most cancer cells, but not in normal cells.