Super Mario Run – Benefits of Completing the Pipe Levels

Yes, it will. I purchased the upgrade on my iPad. When I ran Super Mario Run on my iPhone, after logging in to my Nintendo account, it not only synced the purchase but my progress (levels completed, coins, etc.) as well.

I don't know if it matters or not, but I use the same iTunes account and Nintendo account on both devices.

I've marked this as a community wiki post, because I think this will take multiple data points.

I've played on a mix of cellular and wifi since launch day. On cellular I've mostly played Toad Rally, which would naturally use much more network bandwidth. I've also done some shopping and read the notices/alerts several times. I've probably played about 3-4 hours on cellular (this is a total guess) and I've used 26mb of data, which includes initially setting it up and a partial DLC download before switching to wifi.