It is not infinite because it has an end. Once you get through it all you get to the last page of the Internet (spoiler below):
infinite: NO. Information is energy, and "the internet" is made up of bits of digital information. You would need infinite energy to make an infinite internet, and we've not discovered such a thing yet in our solar system.
can you view it all: I think YES. Someone said the pace at which more content is added is huge, so it's probably a straightforward task to view it all. You can not do it sequentially... one page after another, but if you put enough monitors - say 10000 - and watch it all at the same time maybe... you need enough screens (or people helping you do the viewing) so that you beat the pace of adding more stuff to it.
by the way, I think your intended question was "is the content of the internet infinite?"
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.