Yes power consumption can (and often does) depend on the operands at least to some extent.
Older ARMv4 CPUs made this explicit for some operations like multiplication, where if you added more zeros to the number the result would finish sooner and save not only power but also CPU cycles. This was a very common power saving optimization in those days.
Modern CPUs have even more elaborate optimizations like this, with the instruction decoders checking for certain operand values that can be optimized away. For example, Intel CPUs check for and eliminate certain zeroing idioms, where for example a register is set to zero by subtracting from itself. If the CPU sees this idiom, it will skip the subtraction entirely and just set the value to zero. This article discusses some of these optimizations and gives links to additional sources:
If you mean for randomly selected numbers drawn from all possible register values and not specific idioms or numbers with lots of leading zeros, you can probably assume that all numbers use the same amount of power since you aren't likely to have too many random values that the system can optimize by chance.