Hello,
Well, every frequency has the ability to power something, so yes every frequency harmonic has the ability to power a load. This is sometimes a problem when we want to limit harmonic power.
The OP seemed to be asking the general question if other harmonics can produce power so yes that is correct.
When we talk about power 'transfer' however that's a little different because sometimes we are honing in on one harmonic only and usually that is the fundamental. Sometimes we want to know how much fundamental frequency power is transferred because we wont be using for example the third harmonic for any useful purpose. On the other hand, sometimes we (for example) might only want to know the third harmonic power transferred, and then we would be ignoring the fundamental.
I dont think the OP was talking about power transferred though but he can clarify this if he wants to.