At least in CMOS, the power supplied to the transistor is not being modulated as part of logic operations. Modern hardware does clock gating and power gating of modules for power saving, but that is not what the OP is talking about.
In hardware the equivalent of a ternary is a mux, which can be made from a lot of parallel instances of
out0 = (a0 & cond) | (b0 & ~cond)
Or in other words, both branches must be computed and the correct value is chosen based on the condition.
"Power" was very sloppy language on my side. I was talking about the low voltage / high voltage difference that you get from transistors. A logical gate ultimately has a single output voltage based on its inputs. If its inputs are 1 and 1 (+5V and +5V), its output will be, say, 0 (0V), not "initially both 0 and 1, but later only 1 is chosen".
Similarly, a two bit adder is not going to have all 4 possible states internally or for some time - as soon as the input voltage is applied to its inputs, its output voltages will correspond to the single result (disregarding the analog signal propagation, which I assume is not what you were talking about).
Similarly, a conditional jump instruction will not be implented natively by computing both "branches". It will do a single computation to set the instruction pointer to the correct value (either current + 1 or destination). Now sure, speculative execution is a different matter, but that is extra hardware that was added late in the processor design process.