From what I can find the Phantoms had the 20mm gatling gun mounted under the radome. I remember them being there on the USS Saratoga when we were sending planes into Vietnam in 1972-73. The plane had it's first flight in 1958 and was retired in 1995-96.
The link tells you about the 20mm cannon and show you some picures that makes it pretty obvious that it was there.
I think the AF used variants that might not have had the 20mm cannon, but I couldn't find any reference to the pilots having a problem with no guns. If you can find that article I'd be more than happy to read it for myself.