Yes, a person with cold sores or oral herpes can transmit the virus to their sexual partner's genital area if they have oral sex, potentially causing genital herpes.
It is more common for herpes simplex virus type 1 (HSV-1) to cause cold sores and herpes simplex virus type 2 (HSV-2) to cause genital herpes, but through oral sex, HSV-1 can cause genital herpes