Will searing meat before braising it improve the flavor?
Generally, yes.  Searing the meat will improve the flavor on the outermost layer of your brisket due to a process known as the Maillard Reaction.  It's the process of using heat to chemically transform proteins and sugars into new complex flavors.  This process creates the &quot;crispy&quot; layer found on steaks and burgers and releases the smells that make your mouth water.
While this flavor will only be present on the outside of the meat, it will help to season the broth/liquid which will penetrate the brisket as it cooks, flavoring more of the meat.
I would be cautious when searing after using a mostly mustard based marinade, as the mustard could possibly burn before getting the desired level of sear.
As far as removing the meat from the braising liquid, the flavor will not be affected as much as the juiciness of the brisket as well as the continued cooking time.  Air cooling a brisket will cause the meat to cool much more rapidly compared to cooling the brisket and liquid together (since the liquid must cool as well, it will take longer).  This continued &quot;cooking&quot; during the cooling process will help to break down the tough connective tissue, which briskets contain much of (hence the reason that most briskets are cooked/smoked for 10-12 hours).  If the brisket turns out a little tough after after air cooling, you can braise for a longer period to overcome the toughness.
If you do choose to remove the brisket from the liquid to cool, I would recommend to wrap the brisket with plastic wrap to help the meat keep all of its precious liquids!