For our actual conscious experience though, there's some evidence that we're very noise tolerant. I can't find the paper now, but one recently just came out showing that at certain parts of the brain you won't even notice an electric shock.
I have a disorder that's very relevant to this, it's called visual snow syndrome. It's poorly understood but the current theory is that the brain has a fair amount of internal noise which is suppressed by a filtering mechanism but in some people this filtering mechanism fails, making the brain's internal noise becomes consciously perceptible. It looks like a badly tuned analogue TV for the most part with lots of static (hence the disorder's name), although other things like haloes around objects and geometric patterns appearing in textures like bricks are common too. Less fun is the permanent headache, sensory overload issues, and often a whole host of other neurological issues.
It's one of those unfortunate cases where medical professionals palmed it off for decades as patients making it up for attention. I was personally told as a teenager to "try and imagine it away" by a neurologist which of course was utterly useless advice, and I was also given antidepressants at one point which made it infinitely worse, wouldn't wish that experience on my worst enemy. Fortunately I ended up in the care of a neurologist who finally recognised what it was and gave me a formal diagnosis after doing some scans to make sure it wasn't a brain tumour or something equally unpleasant. It turns out that although nothing shows up on a normal MRI scan, if you do an fMRI scan of brains like mine you can actually see the differences that cause the brain's noise to leak into your consciousness. Weird stuff.
Is it similar to the kinds of visuals a person using psychedelics might experience?
I definitely think psychedelics have a role to play in understanding these dysfunctions of the visual system, although unfortunately my country (the UK) has a very unenlightened view when it comes to banning things and firing chief scientific advisors when they point out that there's no real scientific justification for prohibitionism. Vernon Dursley is apparently the target voter for both major parties!