Yes. In curing circles it's known as a 'combination curing' method. Injecting your brine (10% to 12% of the meat weight) , then covering the meat with brine allows for curing from the outside in, and the inside out.
Cure #1 has a number of functions. It provides the 'cured' flavor (think roast pork verses ham), it provides for the pink color of pastrami (or corned beef), and it provides a level of food safety during the long curing times, and if you used low smoking temps.... Cure #1 would add a safety net there too.
There are two approaches to pastrami. You can cure a brisket flat (salt, sugar, Cure #1), then season and smoke to make pastrami. Or.... you can corn your brisket flat (salt, sugar, Cure #1, and aromatics) then season and smoke to make pastrami. I like the back-flavor of corning using all the aromatics, and then making pastrami. But both approaches make wonderful pastrami because the pastrami rub (pepper, coriander, garlic) form the base of a pastrami flavor.
I'm curious why your store-bought corned beef disappointed you when you made pastrami? If it was the 'corned flavor' you might be better off with a home cured brisket rather than a home corned brisket as your stating point for pastrami.