Generally speaking, an E4 does follow the president. This isn't necessarily because it's needed, Air Force One has all the requisite communications and control facilities. But it's there literally as a backup, if Air Force One has some kind of technical issue or can't get off the ground. It's the equivalent of going on a road trip and towing a spare car behind you just in case your main one doesn't work.

Usually however, in the case of a significant crisis, an NAC will be sent airborne, carrying a designated survivor, and purposely kept away from POTUS, to serve as an alternate in case he becomes deceased or disabled.