Sure, but could the work not be distributed amongst many users? How many concurrent users would it take for it to be useful? Would likely demolish battery life and data caps, but I think you could run only when batt > 50% and wifi is on.
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.
According to bitcoin.it [1] iPhone 3g's cpu (ARM1176JZ(F)-S) can achieve 1.19 kH/s
When I plug that into Alloscomp's bitcoin calculator [2] it says that at todays exchange rate you could expect a return of about $0.02 per month per phone (assuming they're on 24/7)
If you had one billion devices you would make around 30 million per month. One billion devices is totally unfeasible though (Especially one billion on 24/7) and you could definitely make more money some other way with that many devices.
