It would depend on how bad the TV sounds and how good the radio sounds. The radio may not be stereo as well.
Most FM transmitters these days are for auto use so you would have to add and adapt a 12v dc power supply.
I doubt it would be worth the trouble.
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.