I kind of doubt configuration will copy header text to all the items in the same document but hey, what do I know - I'm just an ABAPer. 
We have a user exit that does something similar. The routine is called in USEREXIT_SAVE_DOCUMENT. The important part is that it's called using ...ON COMMIT. I suspect this was chosen because the texts need to be updated already by that time (this was developed by a consultant long time ago). Then further down in the routine the regular text functions (READ_TEXT, SAVE_TEXT, etc.) are called.
You'll need to also think about a scenario when users (hypothetically) enter some text in the line items manually. This will need to be handled somehow.
Another option would be instead of copying text (this is not good for your database, by the way) read the text when creating subsequent documents and add it at that time. Or, even better, if this is just needed for some form then just add some code there and read the text directly from the order header or wherever and avoid this whole hassle altogether. Many choices here.