Pulled pork - inject brine AND immerse in brine?
Frankly - if you're aiming for pulled pork, brining at all isn't really necessary. Brining is most beneficial for lean pieces of meat because it helps the meat retain moisture and prevents a lean cut from drying out during fast cooking. 

When slow-cooking a pork shoulder, you're going to wind up with very (deliberately!) overcooked meat fibers with much of their moisture squeezed out. The apparent moisture comes mostly from rendered fat and collagen converting into gelatin, which aren't really affected by brining; they are functions of the long and slow cooking process.

If you like the flavor that the brine introduces, then you can sure keep it, but given the other processes involved, I would not expect any difference in brining method to produce a noticeable difference in your pulled pork.