Of course you can view it all.
The National Security Agency is aware of this, and has for years been ghosting every bit of internet data onto storage. They have huge facilities dedicated to this one process. They are literally recording the entire internet.
That includes all posts on these message boards. It's completely illegal, but all major web companies and ISP's are cooperating fully, including google, facebook, twitter, AT&T, Comcast and Verizon. Very few people know of this and even fewer care. Rest assured that everything you've written or done on the internet in the past 10 years is recorded on an NSA server, and can be used against you in the future. That includes private things like emails. It's how that FBI agent got Petraeus's emails. It doesn't matter if you delete it, if it ever existed, the NSA has it.
It is a staggering amount of data, and most people assume it's technically impossible to do, but they really can record it all. Minus maybe a few hidden IP's that search engines don't notice, or traffic that doesn't pass through any American facilities.
Can you view it all, certainly if they set up a bunch of monitors displaying the data in binary form, then you'd be viewing it all.