Personally, I believe that it's another one of those confidence things. There are all kinds of sounds in the water, especially with all the traffic nowadays. Also, I would ask what it does to the fish? Supposedly it will 'spook' them - drive them off - correct?
I think that if you are on some body of water that get's little to no boat/electronics/noise pressure, it will certainly have some type of effect. Otherwise, I don't think that it matters.
Recently, we fished a tourney at a new lake (for me), with a tremendous amound of blowdowns in the water. We were in a shallower area (5-8 feet max depth), fishing around the blowdowns and such. I was running the trolling motor, moving around and fishing with a partner. I had both the front finder on (Matrix Unit - newer), and the console finder on (older Eagle).
We had been in this one are, fishing around a big blowdown. We fished it for about 10 minutes with no real success. The wind blew us in an area that we got somewhat hung up on a major limb. After trying unsuccessfully to 'gently' move away, we then had to bump and grind to get out. In doing so, I really belted the tree limb hard. Parter on the back shouts out - 'there were at least 10 dinks in that tree that scattered like the wind when you hit that tree'.
The electronics didn't seem to bother them at all, in this case.
If you believe that having it off helps you, then turn it off. Personally, I believe that you are limiting yourself not to have one of your 'tools' working for you.
Tex