Internet: On Nimitz, all have internet access, but depending on operational status, we shift to "tiered usage", in which, usage is controlled by tiers. For instance, the bottom tier is pretty much shipwide usage. The next tier up will eliminate anyone E3 and below. The next tier is CPO and above....etc. So you will have internet to some extent, and email pretty much all the time, although the limiting factor there is computer time, which is generally limited during the workday. That said, barring EMCON levels, you will be able to check your email every day or so.
For essentially useless, I am not sure what you mean. You didn't hear it from me, but I have seen guys buy cars from the Persian Gulf with their reenlistment bonuses, manage bank accounts, buy stocks, you name it.
Instant messaging will be hard, and guys will be pissed you are hogging up computer time to IM with your family vice emailing them, if you could even get AIM express to load.
Oh, and we are in 8 section duty (again) after testing is over this month. Eight section! My buddy at Point Loma sub base stands 3 duty days in the same period that I stand one!