If (when) food is irradiated, would it have to be labelled that it has been irradiated?

It will depend upon the laws of the country where it is sold. In Australia it is labelled as "containing ingredients treated with ionising radiation." In Canada if the food is packaged it will state if it has been irradiated on the package, and if it is fresh or unpackaged the retailer must display a sign next to it. However there are about 50 countries which irradiate food so some of them probably do not have labelling regulations.