*** THIS IS A HARDWARE ISSUE ***
I just had my iPhone 4S swapped at my local Apple Store and the static is GONE. I have verified this across multiple phone calls. This is NOT a network or in-call issue, as the static noise is being generated inside the iPhone 4S itself. You will note that this problem is nowhere to be found on non-4S models, which rules out iOS 5 itself. If you launch a data-intensive app using only 3G data and hold the back of the phone (apple logo area) to your ear, you will hear the buzzing coming from that area. The reason it is heard during calls is because the speaker opening aids in transmitting this noise from inside the case.
I don't know if it's possible to examine what components are in general proximity to the center top third of the case, but I'll bet it's a transmitter or receiver of some kind that is causing audible interference. Or perhaps that might be the location of the Qualcomm 3G chip(s). Remember the 4S has a new antenna design and also supports higher HSPA+ speeds, so it has some major changes on the wireless/antenna side.
I also wonder if this also relates to battery problems. My understanding is that iOS 5.0.1 addresses battery drain while in sleep/standby mode, but does not address the rapid drain during a call or while using data. I don't know much about electronics, but the buzzing may be causing excess current to be drawn from the battery during 3G use, explaining the rapid battery drain when using the phone. I would place my bets on a bad hardware component, as a software update surely will not solve an electrical buzzing that's emanating from the circuit board.
Again, swapping out my phone has solved this issue 100%.