Can the AI write a first draft of a section I added, such as a special offer page?

Yes, from version 1.9.24. Open the section in the editor (hover its row on the book's page and click the pencil icon). In the box at the top, describe what it should say, for example "20% off my course with code BOOK20 at [link]", and press "Draft with AI". The draft is written into the editor with your book's AI engine. Facts you did not give, such as prices, links or dates, come back as [placeholders] for you to fill in, so check the text and replace them before you export.