Is it normal for a switching power supply plug to make noise?

Yes it isn't a problem. A lot of answering machines use a voltage adapter to limit the amount of power that is supplied from the mains socket. You often get s buzzing sound from adapters like this that restrict the flow of electrical current. Similar to buzzing from a light switch that uses a dimmer to lower the lights [uses restricted current too]

However if you machine has just a normal mains plug with no adapter or inline module for restricting electrical voltage then it might be a good idea to get the machine checked for safety reasons and piece of mind.