Hi @Ed112, thanks for reaching out! 100% - I think that this would certainly work. You could have the separate Backlogs and Sprint Boards as mentioned and have one main Sprint Board (maybe with a custom field highlighting the subteam - similar to what is highlighted in this video) with everything in a sprint from each subteam multi-homed (which could be triggered through a rule).
This additional Asana in Practice video on Rules may help you out further with this. We also have one coming very soon on Multihoming so feel free to stay tuned!