The receiver has an S-Video output which goes into my TV. I worry about having the output of hi-fi receiver running through the $30 box before getting to my TV.
You are absolutely correct about that. The $30.00 box will, without question, degrade the video signal.
S-video separates the luminance and chrominance information into different cables, allowing more resolution and bandwidth for each. Composite video (which I assume is what this box uses) doesn't have this separation and therefore has lower resolution than S-video.
Such a device would not work at all in my home theater system because I have DVD running through YPrPb component video, and HDTV running through RGBHV video.