Any process that produces apoptosis will affect RNA one way or another,because during apoptosis more than 500 enzymes are in charge of proteolysis of cell components and also of Ribo and Deoxy ribonucleic proteín..
i dont think it will create major problem..Since most of the drugs cause double strand break...So RNA is safe...but thomas has point . Still reports suggest that apoptotic gene expression goes high upon chemotherapy.