It is not uncommon for shipping to take place ahead of time providing a tracking number. Most of the time these devices are held by FedEx until launch day. This happened to me a few years ago. It's possible they will get them early, but it doesn't usually happen that way!
There are literally hundreds of reports on /r/GalaxyNote8 and xda-developers.com of individuals receiving shipment notifications from Verizon with delivery dates of 9/5, with orders placed as recently as 9/2.
I'm one of them and happen to have been an erstwhile Note 7 owner. The same is not true for all reports, however; some have switched from other providers, and others are already VZW customers but not previous Note 7 owners.
Shipment this early before the official release date is somewhat atypical for Verizon, but not unheard of. I do think (in this case especially) it will generate a great deal of goodwill with their customers, and at the same time keeping those that actually have Notes in-hand on the 5th from paying much attention to Apple's 9/12 announcements.
PS. BGR.com claims to have an official response from Verizon that the Note 8 is shipping early.
Don't hold your breath folks. This is SOP. Carriers take the orders and release to Shipper, who is not allowed to ship until 2 days before the release day of 9/15. Some will arrive a day early, just luck of the draw.