I would like to hide an unsightly wire by putting it in a copper tube
no, that is ok, but might not conform to code. It would be easier, and conform to the electrical code, if you used electrical conduit, which is a tube of metal. .
no, the copper tube will not have any contact with the conductive material of the wires, in fact the copper tube will cancel noise from the wire if u ground the tube, your current will not be affected
If you are putting the 2 wires (life and neutral) and they are WELL insulated. there is no problem. But for safety reasons I would also ground correctly the copper tube so that touching the tube won't be dangerous if for some reason the insulation becomes damaged
The copper tube will not affect DC current nor low frequency ac current. It may or may not affect rf current depending somewhat on the spacing between the insulated wire and the copper tube, the length of the copper tube and also the frequency of the rf. For instance it might affect the reception on a radio or television receiver if you ran the unshielded antenna leads to to the receiver through the copper tube.