A nuclear battery is not actually a battery, it's a generator. Trying to run something purely off a generator is stupidly inefficient because you'd need the output potential for the max load at all times even when on average the load is much lower. You absolutely want to pair a generator with a battery. Even power plants have batteries to store excess power.

If you think a little past the name misnomer it's obvious that this would work by pairing it with a smaller battery to handle spikes in usage. The end result is still the same though, you'd have a phone you'd never have to plug in.