She will be denied at the border since China does not allow outbound travel using a Chinese passport when the final destination is Taiwan, even if you transit on the way. She must find some way to hide her ultimate destination from the border police. Fortunately, I don't believe the border police has visibility to her final destination, as long as she only shows the boarding pass for Hong Kong.

However, this further complicates things because she is not allowed to fly directly to Hong Kong using a Chinese passport either. She must use her Hong Kong and Macao Travel Permit at the border, or show a fake itinerary out of Hong Kong to a third country that is not Taiwan (along with the visa for that country if it's not visa-free).

In other words it's a world of pain to book a through-ticket to Taiwan from China using a Chinese passport. It's much easier if you book two separate tickets.