There are nuclear batteries available, but the amount of power they put out is in the microwatts. Not exactly a useful amount of power for a modern phone. Good enough for some kinds of sensors, though.
Yeah, while the basic concept obviously would work I can't see the energy density they are claiming. C-14 has a long half life, the decay rate is going to be low.
I feel compelled to note that diamond, far from being a "virtually indestructible" vibranium-style material, is in fact made of carbon and is therefore highly flammable. What happens when this battery catches fire?
