To my knowledge, my customers are receiving my invoices. I want to use this smart folder that gathers in one place all the copies sent to me as a way of quickly checking at a glance who I have and have not invoiced, without even having to login to QBO. It will be evident in my email program. 
Regarding your second suggestion. I have already had two calls with support, the second of which, last week involved a screen share and they were stumped. But they did say this is something that the engineering team is working on and they linked my case number to that project. Apparently, I'm not the only one experiencing this problem. Hopefully with my case linked, when they find a solution, I'll be notified.