Yes, high currents create an audible hum, but not in a home- only on the contact points in transformers. If you're referring to the electricity in your home then no; youshould not be able to hear that. Audible electrical hum is something you get in substations or transformer pads, not your home. You are likely hearing something else.
If it’s a small buzzing sound in your house it might be a open/faulty wire. If you hear it whenever you’re in a spot with no electricity then it’s likely tinnitus. Either way it’s bad