When done properly, the analog signal will be delayed to correspond to the digital signal, and that would, of course, include analog radios. Because the digital signal has to link, the analog and digital signals are supposed to blend perfectly. If you've ever listened to an analog station blend to digital without a proper delay, it really hurts your ears!
When using "live mode" with HD Radio, the analog broadcast will be live, and the listener has to manually link to the HD signal if (s)he wants digital. Otherwise, the HD Radio will just air the analog signal. The only reason one would typically switch to digital in that situation would be if they wanted to listen to a subchannel that wasn't already saved as a preset. Otherwise, the main channel won't blend perfectly and will be running behind.