Yes. Romulans should at least have the option to sport the long chin hair you often seen on elderly Chinese. I think my former Romulan Senate member to have a distinguished look such as that. Examples below.
For Aliens (You actually needed to be Alien before getting a quasi-Romulan species), you are able to add facial hair to the Romulans. However, you lose the Subterfuge and Romulan Operative, if you went for the alien customization, but at least you get some nifty traits in return.
With the addition of Romulan features in LoR, you can easily get facial hair on an Alien species on both Fed and KDF factions. However, I don't know how you can manipulate the limited Alien Gen to get facial hair on a Romulan.