Well actually, I've been told that the problem of rail noise comes from improper maintenance of the rail track, not the motive nature of the cars themselves. Noise on BART is due to a liberal application of NIH. BART literally reinvented the wheel – they used flat profile wheels (nobody else does this) which dramatically increased noise and wear. BART also spaced the tracks too tightly in turns further increasing noise and wear. They made their cars out of aluminum to save weight, creating a bit of an echo chamber (this got worse once they removed the carpeting). Caltrain doesn't have the luxury of lightweight rail cars since they share tracks with freight service.
BART doesn't bother greasing the tracks like nearly every other rail system (almost certainly an artifact of their homebrew train control system). Unfortunately while reinventing everything they opted against decoupling the wheels from each other (a.k.a. using a differential like a car or truck might).
Oh and let's not forget the Oakland Wye, BART's testament to noise, poor service, and political dysfunction.
Simply put BART can't really grind the rail fast enough to keep everything quiet for a meaningful period of time (if they could I assume the wear on the tracks would be astronomical). BART also needs custom rail grinders and whatnot because hey why not throw a custom track gauge into the mix.
So actually, just a change to electric cars will not maintain quiet operations
Caltrain is fairly quiet, at least inside. At the very least the electrification will certainly help with noise while stopped at a station.
I encourage anyone to go ride the high speed rails of Germany, France, Italy, China, Japan, Korea, to understand what properly maintained rail is capable of feeling like. Or even the U-bahn in Munich, Frankfurt, too.
Spain is missing from your list, they were instrumental in getting the Pendolino developed and, IIRC, have more high speed track than any other European country.