In that case you wouldn't notice a boost in display quality, but you would however (supposing your GPU has a HDMI output) get both your video signal and an audio signal going to the TV using the same cable so you could use the TV speakers.
It really makes no difference if you buy a cheap HDMI cable or an expensive HDMI cable when it comes to short runs. HDMI is digital, so it will either work or won't. The only thing with a cheap cable is it might fall apart, but I highly doubt it.
VGA is analog, so you could have interference or degradation of the signal. I sorta doubt this is happening, but you never know.
For $5 I'd take the chance and see if it improves your picture quality.