Do the three wire that run from the aircond unit to the aircond compressor carry current?

What three wire is that?
What kind of unit? Not every on is the same as the one you have.

The basic answer is most likely. ALL wires carry current of some sort at some time. That is their reason for existence.

This statement,


ALL wires carry current of some sort at some time. That is their reason for existence.

Would be my answer.

Otherwise why have the wire?

A little more detail as to what you have and why you ask would be helpful.