Does AR 670-1 cover the use of aftermarket civilian body armor?

NO ist doesn't, but you are supposed to wear issue only. The common sense answer is you are to wear what is issued and allowed only, should you be wearing a civilian copy and get injured due to poor quality of not meeting mil spec then that can and may lead to bigger problems for anyone that has GEARDO syndrome.

I don't want to sound condescending, however civilian body armor is not up to mil spec despite what the label indicates..why would you want to wear armor that, at best, may stop a 9mm round?

So I found the ALARACT message that addresses this. The short answer is NO. Sorry it is from a 3rd party site.
http://www.teamwendy.com/wp-content/uploads/Army%20Safety%20Message.pdf