Yes and no, it’s not about the instruction set size but about general overhead.

The x86 architecture makes a lot of assumptions that require a bunch of circuitry to be powered on continously unless you spend a ton if effort on power management and making sure anything not currently needed can go into idle - for mobile CPUs there’s a lot of talk about “race to idle” as a way to minimize power consumption for this exact reason, you try to run everything in batches and then cut power.

The more you try to make ARM cover the same usecases and emulate x86 the more overhead you add, but you can keep all that extra stuff powered off when not in use. So you wouldn’t increase baseline power usage much, but once you turn everything on at once then efficiency ends up being very similar.