Radio you are talking about is a reciever.
No problems there. Handheld (walkie-talkies) are problems. Security personell are notorious using these next to PLC's.
Dealt with a case once that drove us nuts for almost a month. Turns out the watchman was doing a radio check on his rounds right next to a PLC at 2am every morning. This kicked the PLC out of RUN mode and they had to wake the tech up and have him reload the program into the unit. When he keyed the Microphone button, that would send enough RF to give the PLC an identity crisis <grin>