It should work
They're the SAME CABLES
If you do get bad video, you may want to invest in better cables or a better switch box.
But as far as the signal goes, it's the same cable.
Red(video)/Black, White, Yellow, Green, Blue, Red(video) all use the same type of cable.
It's just a metal wire (2) that completes a circuit. Nothing fancy.
Component cables aren't special.
Composite cables came about because we didn't want to use component cables.
OMG THREE cables for video? NO NO NO.
Let's just go ahead and fold R G B into chroma and luminosity.
That way, chroma tells us the ratio betwen the colors, and we can get how red, greeen, or blue an image is, yay.
Luminosity will tell us how bright the image is. Oh joy.
But we've still got two cables. Let's go ahead and do a little math, some very simple signal processing, and slap them together.
AH! We've got an image! It's...well, it's much crappier than what we'd have if we went with the logical R G B method, but, consumers will love us!
And then we can separate some of the signal out for a future cable, (s-video) and then restore it completely over several decades.
I'lls top now, but yeah. Should work fine. Unless there's some frequency / range limitations on the audio parts of your switch box. Shouldn't be.