No there is no known link.
It is only conjecture that oral HSV1 could play a role in the facial nerve paralysis. Bells palsy itself is not a specific condition but a 'residual' explanation once other causes of facial paralysis are eliminated. It is likely there are a number of possible causes and HSV1 could be one of those.
However it cannot therefore be inferred that a person with Bells palsy has oral HSV1. It certainly cannot be used to infer a genital herpes infection.