You could do either. I don't think it matters where your bind off ends. If you'd like to use the tail of yarn to seam the two halves of the collar at the back then bind off so the tail winds up at the neck. Just take good notes so that you can knit the other half for the same number of rows.
I'm kntting a shawl collar right now too but the collar is knit separately and then sewn to the neck edge. Much eaier the way you're doing it I think but we'll see how this goes. Good luck finishing yours and post a photo if you'd like. We all love seeing finished projects!