Probably but... Olive leaf extract appears to be a broad-spectrum anti-microbial, effective against a wide variety of viruses, bacteria & fungi in the lab. I haven't found any published clinical studies on it for herpes but many patients claim it helps. While more research is needed it's safe to try. I'm more impressed with topical melissa (lemon balm) for herpes-see http://www.Med.Nyu.Edu/content?Chunkiid=21570.
Safe to try. I couldn't find anything in the nih database, but there's an online claim that one "private" (i.e., unpublishable) study "showed" an effect. Herpes infection is serious and your physician can help you manage it; unless he/she objects, you're free to supplement with olive leaf as well. Good luck.