I agree you're limited by the output of the TV and the performance of the radio. Keep this in mind: There are audio bandwidth limits for FM, mainly in the 'treble' area, so you won't get real 'Hi-Fi'. That being said, I'd still give it a try, you might be very pleased.
Here's another thought. Does the TV have a headphone jack? Does the Panasonic have an AUX input? This involves a simple cable connection, if you may consider that. The sound quality may be better.