Only partially, because the US military protects more than just the US dollar banking system. For example, the US military protects the united states and everything inside it.
Bitcoin mining only protects the currency and since Bitcoin is exactly like fiat in the sense that it is just a ledger that allocates resources, it is entirely dependent on the physical world that the all the militaries around the world protect. Do we count the US military towards Bitcoin's impact on the climate? It would be justified.
Clearly not all of the military should count towards the dollar’s climate impact, not even close, but some of it wouldn’t be needed without the dollar, and that should count.
What portions of the government and military could be dropped if the US dollar hegemony didn’t need to be maintained? What could be dropped if we didn’t need banks to handle money?
This is of course impossible to quantify accurately, but it shows the picture isn’t as simple as “ban BTC because it uses more power than Argentina”; an angle that’s thrown around a lot around here.