- Yes. Indeed.
Remark The way I interpret your question is, is: "What's the the value of the PSD (Which you refer as power) frequency". The answer to that is that many people dealing with White Noise try to understand if they can intuitively think it is built by infinite sum of Harmonic Signals. Which actually the definition of White Noise: It requires all basis functions in order to build it. Each with the same for any frequency binpower (On average). - In case you'd see such signal it will indeed have infinite power. Yet you can only encounter Band Limited White Noise which is white within the frequencies it was sampled. See How to Simulate AWGN (Additive White Gaussian Noise) in Communication Systems for Specific Bandwidth.