I would be surprised if that's the case. Why would memory ordering have any effect on power consumption?
[1] https://www.anandtech.com/show/15871/amperes-product-list-80...
Having a cache coherence system which was itself weaker, allowing reorderings consistent with the memory model, makes barriers and "implicit barriers" like address dependencies very expensive, and there is little evidence this is the case.
Even in a hypothetical core which had a cache coherency system coupled to the memeory model, you aren't really avoiding any coherence traffic, just allowing certain reorderings such as satisfying requests out of order.