Hello, Cousin Chuck:
Yes, I believe that's the case since most of Company B enlisted there. In addition, I believe the exodus of the "redgement" refers to it leaving Camp Hope for Mulberry, Mazzard Prairie, and eventually Prairie Grove. You probably remember that McRae had prepared to march toward Fort Smith earlier, but received orders on the morning of departure to go toward the White River instead. The return trip to Camp Hope/Nelson might have been the fourteen-hour march Private Corder referred to. It sounds as though he spent a lot of time just chasing the regiment after leaving his family.