Yes, but the stuff that people find most objectionable- the Fox opinion shows, Hannity etc- have their home on Fox-the-cable-channel. They might get picked up on some Fox affiliates (though I doubt it, they're the special sauce that gets people to pay for cable), but the engine of the thing is the cable channel.

The programming on Fox broadcast channels is different than Fox News, which is specifically transmitted via cable or satellite and, legally, not via public airwaves. Fox broadcast channels are subject to the same laws as other broadcast channels.