Chris, thank you for demonstrating for the Community the importance of reverse-planning SV cooking for large items. That's planning your scheduled times of cooking steps back from finishing and service.
If you left that brisket whole, that's one challenging hunk of meat to cook in water. Could that explain the dearth of recipes?
To answer your question, you can cook today and smoke tomorrow if you do it safely to prevent any food born illness. i would never recommend a two-stage cook for any thick piece of meat, particularly with an overnight time out interval. You don't reveal your plan for the brisket between SV cooking and smoking, but it deserves serious thought about what could happen to your meat during that interval. If you don't have a plan, i'd rather not consider the potential consequences.
It's important for food safety reasons to limit the time your meat is in the food temperature danger zone. The US Food Code requires food can only be between 41F to 130F for less than 4 hours in total.
Here's what i recommend you do.
Skip the interval between cooking techniques.
At your 6 PM finish, don't finish.
Keep your circulator operating but drop its temperature setting to 132F. That maintains your brisket at a safe temperature while only marginally increasing its tenderness without altering your planned degree of doneness.
In case you think i am unduly messing with your planned cook too much Chef Thomas Keller of The French Laundry restaurant and SV cookbook fame SV cooks his briskets at 147F for 48 hours. Unless you grievously oversleep tomorrow your brisket will be just fine.