On my 1st shoulder in the #2, I thought "Why not do both?". I did. It was very good. I then tried it with a brisket. It was absurdly good. My wife prefers slow cooked shoulders in the dutch oven, so I haven't done another in the #2 since. However, I have done quite a few briskets since. The last brisket I did, my injector broke. So it only got a swim in an equillibrium brine for 3 or 4 days. My wife asked after if I did something different. She said she thought it was equally tender and moist as when I do both brineing & injecting. However, she thought the flavor was much better when I do both. I agree 100%. It was great but not absurd. Therefore, I believe the brine has more effect on the the tenderness, moisture & causeing the fat to turn in to something special on a brisket. As well as adds some additional flavor, but with limited penetration. The injection is a great way to get deep flavor penetration as well as aids in moisture retention.
These methods both imorove upon a naked primal cut, individually. I find, particularily with brisket, useing both amplifies flavor & moisture retention. It is by no means necessary, but I think, well worth while. And I leave you with this question, Is there any way it could possibly hurt?
To answer your question, 1st brine (rinse & dry when complete), 2nd inject then apply binder & rub, 3rd wrap & rest.