This paragraph suggests that the ability of BET inhibitors to re-activate latent HIV would not be expected to occur with HCV. According to this source, HCV doesn't enter the nucleus and does not integrate into the host genome. I'm no virologist, so I'm not claiming to be an expert here.

"In the past twenty years, two newly described human viruses, the hepatitis C virus (HCV) and the human immunodeficiency virus (HIV) (one infecting the liver and the other critically weakening the immune system) have dramatically awakened our understanding of just how fragile is the relationship between humankind and pathogenic microorganisms. These two viruses are similar in many respects. Both viruses have a single-stranded RNA genome, they both have very high levels of viral replication, they both cause chronic subclinical infection that can persist for many years, and they share similar routes of transmission. However, HIV and HCV are also different in many respects. One of the most important differences between these two viruses is that HCV does not have a nuclear phase during its replication cycle and it does not integrate into the host genome unlike HIV. Nuclear phase means that the virus goes into the nucleus of the cell. Both HBV and HIV have a portion of the life cycle that occurs in the nucleus, while HCV does not. HIV can integrate into the host genome and HBV can survive as a closed circular coil (referred to as "ccc"). At least, theoretically it should be possible to eradicate HCV more easily than HBV or HIV. Based on this fact, HCV eradication from the body should be much easier to accomplish than eradication of HIV. With the recent introduction of a new formulation of interferon conjugated to polyethylene glycol, pegylated interferon, many HCV-infected individuals will have the opportunity to be "cured" from HCV infection."