If your building block includes a section break then it automatically includes header/footers. Therefore you can include a section break in your building block to also include the header and footer that goes with that content. The drawback of this is that the subsequent/final section of the document will retain the page setup and header/footer that was already present before the building block was inserted.
The mention above of the Cover Page functionality gave me a lightbulb moment
. You could store each of your 'letters' as a building block assigned to the Cover Page type in order to provide a simple non-code method of inserting or switching letter content in the document. The Cover Page building blocks don't need to be a single page - they can contain multiple pages of content if your letters are like that.