Im not positive, but if you just need a device that plays AM radio, this will do that. It would be a little bulky if you have to hold it or clip to your body though, so would probably only recommend if it can be rested on a stand.
Where I live, the TV stations do not broadcast on the AM radio frequency. Maybe certain AM radio stations are picking up recorded TV broadcasts and re-playing the audio on their AM station. Otherwise I wouldn't know the answer to your question.
If you gym sends the signals, this picks up AM, FM and weather. So it would work great. The old one that I have could pick up tv audio when local stations we broadcasting over the air, it was great for listening to Leno's monologue...but alas no more.
You use to be able to before all the televisions went Hi Def. I use to be able to listen to the news and TV shows, but not anymore. The radio is still good though, I love it. It is small, portable, and reception is good.
I am afraid where I live the TV is not broadcast over the AM. I find the unit very good - it has a belt clip and is lightweight. You can lock the station so that it does not drift whilst you are moving. If you can get an answer to the TV issue, I think it probably would be suitable for use in the gym. It is not much bigger than a larger stop watch and so is quite compact.