I don't believe it can be done, at least not with any simple combination of ID features. Parent pages are a peculiar mix of being tightly bound to their document pages AND completely disconnected entities, at the same time. Users would like many features and aspects such as having a Parent page follow a selected paragraph style, but their placement in the page array is fixed, not flexible. It can carry a page numbering marker, but autonumbering will not update — which you've probably already found.
Having the CHAPTER frame on a parent page and disconnecting it on the document page so you can type the current chapter number doesn't seem like an overly difficult process to manage, but no, it's not automatic.
You could flow a text file through those text frames, containing an manually-numbered or autonumbered series, similar to the non-standard page numbering schemes. (Put a text frame where you want it on the parent page. In the first use of the page, flow the numbering text file into that frame. Each iteration of the page will have hte next paragraph in the frame.)