Nah you would be given a dosage large enough just to kill the invading virus. It could hurt the person, but killing them is unlikely. Actually wrote a paper on a something similar I came up with back in undergrad using HIV.
But let's suppose that you can't measure in advance the number of cells that are infected, nor can the drug actually tell the difference between infected and not-infected cells (due to the aforementioned genetic abnormality.) What happens when the drug kills too many normal cells? The human dies.
Still it would likely be a staged treatment that wouldn't kill the entirety of infected cells in a single dosage. The benefit is that you could see if there were adverse reacts before continuing.
Radiation is targeted and not administered 'generally' like a drug would be. If you could aim drugs, chemotherapy would likely change drastically.