If I choose to only study the mandatory kanji to write will I be prompted to write later if the word is reintroduced in the textbook in a later chapter's kanji section? Or did I miss out on ever writing the word?

You can always change the option back, and then set the list(s) to start adding back from the beginning (through the 'Change study settings' option on the list's page), which would rescan over the list and add anything that wasn't added previously, catching up to the list's adding progress.

That wasn't exactly the question. Maybe an example would be better. Say I have optional kanji turned off while I work through Genki I and the word かく, to write is taught in lesson three. Then later on in the book the kanji for to write, 書, is taught in a later lesson as part of the kanji section. Will I them get asked to write the kanji if the word for to write is taught again. Similarly if I start studying from a separate list that teaches "to write" with the kanji will I then be asked to draw the kanji in skritter as a separate question or will I forever only just see reading/ definition prompts for "to write". Hope this clarifies things better.