[Tuna-Fish]

It would have minimal effect on data usage, as you only ever need to report back when you've found something, and you only need send a 32-byte precomputed seed every ~10 minutes or so.

It would, however, absolutely demolish the battery. This kind of computation is pretty much directly proportional to power use, and modern smartphones are power-limited. So, if you mine at full tilt, the smartphone will drain the battery literally as fast as it can, and get really hot doing so. You can limit the hashing speed, but this will only spread the work over time. It won't change the fact that to get any good hashrate out of the system, you basically have to consume all the battery.

However, all of this is pointless because you'd need millions, possibly tens of millions of concurrent users to match a single modern $1000 mining rig. Computing sha hashes is a workload that fits special-purpose hardware really well. GP hardware simply cannot properly compete anyway. And now as ASICs are driving up the difficulty, you'd be making much less than 1$ of profit for 1$ of electricity consumed.