No, because there is no relation between transaction volume and block production times, and this is a protocol level constraint. The network aims to produce a constant number of blocks per hour, which happens no matter how many transactions are available to be included in that block.
Here's an example: If, say, the maximum block size was doubled so they could hold twice as many transactions, this would cut your energy usage figure in half, but actual energy consumption by miners would barely change at all. Similarly, if the maximum block size was halved, your figure would double, but the energy consumed would not. If there were no such thing as a maximum block size, your value then scales linearly with the amount of transactions that can be crammed into 10-ish minutes of time.
I dunno, isn't that like saying "if planes were all half-empty, the carbon emissions of the plane would barely change, so you can't blame the carbon emissions on any of the passengers"? Yes, the "marginal carbon emissions" of a single transaction is ~0, much like the marginal carbon emission of taking an empty seat on an airplane is ~0, but by this logic nobody on the plane is responsible for any carbon emissions, which is obviously silly, so in lieu of any better accounting method, you just amortize the carbon emission of the plane across the passengers.
If the block size was reduced to, say, one transaction, then the economic value of the Bitcoin network would surely drop, mining rewards would be worth less, miners would quit, and the electricity use would fall. It's the economic value of the transactions that end up rewarding miners; I can't see how people transacting on the chain aren't partly responsible for the miners' emissions.
I can't think of any obviously better way to assign a number to that than just amortizing it across the number of transactions. It's a meaningful number that explains something about how much usefulness the network produces per unit of electricity. Doubling that by doubling the block size (or, halving it by halving the block size) would be a meaningful change!
>But by this logic nobody on the plane is responsible for any carbon emissions
That is strictly true. This is why the concept of a personal carbon footprint (something dreamed up by a British Petroleum marketing team) is inherently inane.
>Doubling that by doubling the block size (or, halving it by halving the block size) would be a meaningful change!
How and why? It would change your metric, but it wouldn't make the network consume one single watt less or more power. Its efficiency is unchanged.
A machine that spits out one widget per watt is less efficient than a machine that spits out 10 widgets per watt. Even if there is exactly one widget machine in the world, it is always turned on and always draws the same amount of energy, one type of machine would produce more widgets than the other. That machine is more efficient. It is more useful for the same energy input. It's a totally reasonable metric to compare widget-producing machines by!
If the bitcoin network is a transaction-producing machine, the more energy it takes to produce the same number of transactions, the less efficient it is. All else being equal, spending more money and energy for the same result is worse than spending less money and energy.
Here's an example: If, say, the maximum block size was doubled so they could hold twice as many transactions, this would cut your energy usage figure in half, but actual energy consumption by miners would barely change at all. Similarly, if the maximum block size was halved, your figure would double, but the energy consumed would not. If there were no such thing as a maximum block size, your value then scales linearly with the amount of transactions that can be crammed into 10-ish minutes of time.