The way people see underwater is different than the way fish see. The species of fish also impact how they see line underwater. I suspect most fish when up close see braid in any color. Some probably don't care or it doesn't register.
I don't think line color matters a bit - as long as you're using a leader... but it is helpful in another way... I long ago figured out that it would be very handy to be able to tell at a glance what size line was on a given spool (particularly with lots and lots of different reels) and more than one spool for each reel - sometimes with different line sizes for the same reel... So... even back when it was monofilament only - My 10lb line was clear, the 12 pink, the 15 fl. yellow, then back to clear for 20lb and so on....
You can do the exact same with braid - and like I said -very handy to be able to tell what size line is on a given reel... Very handy.
Bob, I've learned to do the same with jigs (you'll remember that from my recent jig order!). I try to do it with braid size, but I'm not as consistent--often buying whatever color is on sale in the weight that I want!