No, because Squarespace is it’s own platform. You can probably migrate your content from Squarespace to Ghost. Not sure how much effort that would take, perhaps it’s something Ghost(Valet) can do, or point in you in the direction of a decent Ghost developer.
I suppose what you could so, is host a Ghost blog somewhere else and link to it from your Squarespace site navigation menu. You could probably style it to look the same as your website, but it would be hosted on Ghost. Then you’d just need to import your content. You could probably pay a developer to write your own JSON export script using Ghost’s API: https://ghost.org/docs/api/v3/migration/