AAC converted to FLAC streaming internet radio

"But, if the sound does not improve, why bother with the conversion?"

Compatibility. For example, FLAC is a very popular lossless format but iTunes doesn't doesn't support it. That forces many people to convert to another format. Doesn't apply in your case, but its just a good example of why you would convert to another format.

"Also, the sound quality seemed to be improved."

I believe you, but have no idea why. It could be some way that the signal gets processed making it sound different. Try converting from FLAC to WAV. Many people find that sounds much better. Nothing to loose except HD space.

I understand that you should not be getting better sound with the FLAC file. But, if the sound does not improve, why bother with the conversion?

Also, the sound quality seemed to be improved.

You can convert to FLAC but it shouldn't sound much different than AAC. Since AAC is lossy, you can't get back the info that was lost on conversion. So, when you convert from AAC to FLAC, the file size is much bigger. But what was added is not music. Its something else to make the file compliant with the FLAC format.