The attachment diary group area is not related to anything else at all. This is just to do with external files. It could be invoices or anything. But whatever Diary group you put here, is what Month End will look for in all diaries, if it finds anything with that group, it will attach to the statement and mark the diary as processed.
The "Include Invoice Documents (No related Transactions)" is only for anything that has come through Document Flow that has not had a transaction attached to it. For example, if an Owner'swater bill has been paid by Direct Debit straight to Water Care, you want to send him a copy of the invoice.
Under Owner Statement Run
This is related to any invoice in the diary (Except those that are linked through an external file). If that is set to no, then no invoices will be attached to the statement run.