Yes, similar to countries going all over the world to find gold in years past. In that sense, fiat would require less military since you don’t need to go conquer anyone, just being able to project enough of a threat to stop counterfeiting is enough.
Either way, it’s very convoluted and tough to tease out line item costs, but I don’t think comparing electricity usage is a good proxy.
My point is that, if a country no longer derives its power and wealth from controlling the banking system through military might, rather than freely giving up that power, it's going to flex that military might in other ways to ensure that it maintains that power and wealth. If crypto merely displaces military resources (as I think it would) instead of replacing them (as you seem to be arguing), then it's not really fair to count the military as part of the banking system's energy/carbon footprint.
Either way, it’s very convoluted and tough to tease out line item costs, but I don’t think comparing electricity usage is a good proxy.