Possibly, but not always the case. Think of when you buy a car that has a top speed to 200 mph / 320 km/hr. Sounds wonderful, but short of a race track (or perhaps a few short stretches on the Autobahn) it is irrelevent.
The same goes for the jpeg / RAW argument - if all you do is crop your images to post of a website, jpegs are going to be fine. If you do a lot of post-processing and tweaking, yes, RAW is the way to go.
NO! Not really.
Same sensor records the same signal and unless you apply very heavy handed in-camera noise reduction to create jpegs (a technique with the aptly named "pixel smearing"), that causes a lot of other collateral damage to the rest of the image, the noise will be the same in jpegs and RAW data. You can get the same (actually better) noise reduction in post processing on a RAW file.
I can get a better high ISO, low noise image by handling the noise reduction myself in post, with fewer side effects.