I wasn't certain if this was the implication, or that it was simply understood to be the case. Certainly the 'mirror universe' might not necessarily be following the same/parallel timeline as in other Star Treks, in this case, Star Trek Enterprise. Just wasn't sure if I missed this connection.
Probably not genetically, but possibly by a chain of adoption
In S1x12: Vaulting Ambition, Georgiou's list of titles and style is given as:
All Hail her most Imperial Majesty, Mother of the Fatherland, Overlord of Vulcan, Dominus of Kronos, Regina Andor, All Hail Philippa Georgiou Augustus Iaponius Centarius.
The part of particular interest is in the distinctly roman-looking section of her name. Iaponius is latin for Japanese. According to Jordan Nardino, writer for that episode, he considers that Hoshi Sato took the title Iaponius on her ascension to Empress to "honor her homeland".
Nardino goes on to say that given their different ethnic backgrounds, its unlikely they were genetically related. But in the same manner that most Roman emperors adopted someone into their house to name them as heir, he envisages this is how the terran Imperial throne is passed down and Emperor Georgiou is an unbroken chain of succession from Empress Sato 100 years previously.
This is all qualified as "one writer's opinion" and "not canon until it's on screen" by the source, but given the canonical Iaponius among her titles and styles, it seems reasonable to assume that even if Georgiou is not related to Sato, she is at least trying to link herself to the former empress by adopting such a name.