no it is I think Jane Seymour wife of King Henry VIII, Charlotte Bronte chose the name to accentuate the physical appearance of her character, as she chose Blanche to give the reader an impression of Rochester's flighty light headed lady friend. I think it was a method she had picked up from reading Austen and Dickens.
The 'Online Etymylogical Dictionary' has 'plain Jane' as being first attested in 1912. It also states that 'Jane' was used in the US to refer to a girl or girlfriend from 1906.
It's just good old rhyming - Plain ..... Who else? Jane!
Just used as a descriptive colloquial expression . I don't think it relates to a specific person at all.