Yes, Nasus can go AP, and it truly is viable, even at higher elo games. While regular old Trinity Force Nasus can be quite the house later on in the game, it takes almost half the game's worth of farm and a solo lane to get to the point that he can do this. AP Nasus, on the other hand, is not nearly as reliant on the amount of farm he can get for his Siphoning Strike, and has an easier time farming in general, while doing gargantuan amounts of AoE damage in teamfights.

This build didn't used to be viable, but after the large buff to his Spirit Fire in Patch 1.0.0.123, he can make use of the suprisingly large damage it can deal. Please, don't discount in on principle without first trying it once or twice.

EDIT: After trying this in ranked a lot more, it actually seems legitimate. I'm not going to say whether or not he is better to have on a team than other tanky AP, such as Rumble or Vlad, but it is still pretty easy to win your lane and do work in team fights.

The biggest caveat to him is still the lack of utility he has, so make sure that if you want to use him in ranked, make sure the rest of your team has the hard CC to back you up.

Pros

Much larger amounts of AoE damage lets you truly carry
Farming is easier than ever before
Can still build up damage on Siphoning Strike and Fury of the Sands to mix up damage types
Fairly tanky for an AP Carry

Cons

Still not as tanky as the traditional Trinity Force Nasus
No hard CC means he has less utility in fights compared to, say, Malzahar
Not as strong of a level 1 champ as AD Nasus

I use the standard 9/0/21, getting improved exhuast for the duration increase and resistance reduction.

9/21/0 is possible, and it will make you much tankier at all stages of the game, but the movespeed, buff duration, mana regen, and cooldown reduction will be sorely missed.

Your rune setup can vary pretty easily. I personally like having early HP and resistances alongside some Magic penetration and AP, but adding more mana regen, resistances, or AP are all perfectly legitimate choices.

Soul Eater is an incredibly good passive, providing Nasus with plenty of built-in sustainability without having to invest any skill points. Also remember later on in the game that lifesteal also works with Lich Bane.

Siphoning Strike is Nasus's trademark ability that gets better the more kills you get with it. Though this ability is the cornerstone of most Nasus builds, AP Nasus has other means of damage, so it doesn't have to be quite as farmed to be threatening. If you do get plenty of farm on it, though, it will still hit very hard, and it's low cooldown makes it perfect to reliably proc Sheen and Lich Bane. Get this ability at level 1 to begin farming it as soon as possible.

Wither is one of the things that makes Nasus incredibly hard to solo later on in the game, acting as almost a stun, with 95% Movement and Attack speed decrease at max rank, and best of all, it now can reach the full slow even if the target has tenacity or a CC reduction ability. It is not as good early game, however, as it cost a lot of mana and has a lengthy cooldown. I get one rank in it and wait to max it last.

Spirit Fire used to be considered Nasus's least useful ability, dealing little damage immediately and being easy to just walk out of. Now with the recent changes to how it works, it does about half of its damage immediately and half over the duration, and without a delay on cast. If an opponent stands in it for the whole duration, it will deal 430 + 120% of your AP in an area.
It is still easy to walk out of the AoE, but with Wither or CC from other sources, it will deal a large amount of damage, all while reducing their armor. It also is a great tool for zone control, as enemies will NOT want to stand in it even if you have no AP yet.

Fury of the Sands may not seem to scale very well with AP, but consider this. For every 100 AP you have, you will deal 1% more of their maximum Hp per enemy in the radius, meanwhile turning about 6% of that damage into extra AD to have fun with. At max rank and 300 AP, you will be doing 10% of each nearby enemies max Hp EVERY SECOND for 15 seconds. This ability has everything you need to take on any champ in any role at least 1v1 in a teamfight, with the percentage damage scaring off tanky dps and the large AD bonus and Wither making you a carry or support's worst nightmare.

Exhaust is very useful to add to your low utility in fights, while Flash is, well, Flash. It's THE best summoner spell for most everyone.

Other possible options are Ghost, Teleport, and Ignite.

Make sure to take Siphoning Strike first, since it's never too early to farm up its damage. Try not to use Spirit Fire too often before level 3, as its damage will not be very impressive yet. If you are being denied, though, don't be afraid to throw it into the middle of the minion wave to ward off your lane opponent. Once you have enough money for Sheen, boots, and a ward or two, push the lane with Spirit Fire and go buy. Once you come back to lane, you should be able to farm without difficulty and without to much concern for your mana.

Once you get the 2nd rank of Fury of the Sands, you should be near the end of the laning phase, and people should be grouping up to starting pushing towers and teamfighting. Unlike most Nasus builds, with AP Nasus you shouldn't be scared to stop farming to go push a different lane, since it will be easy to pick up another wave here or there later on. Make sure you have your first tanky AP item, either Rylai's Crystal Scepter or Rod of Ages before you commit to large fights, though, or you WILL be evaporated.

In fights, your main role is going to be to go in right after the initial flurry of initiation and counter-initiation, and burn your cooldowns immediately. It's really very simple: just throw Spirit Fire down on the most enemies, ult, and Wither the enemy carry or whoever tries to get away, spamming Siphoning Strike at anyone squishy that is in range. Your burst is much better than most people will think, so don't be afraid to flash in order to catch up to an escaping Ashe, etc.

After a teamfight or two and a few tower kills under your belt, you should be able to afford Lich Bane and Rabadon's Deathcap, at which point you can start pushing towers down in only a few uses of Siphoning Strike. At this point, 1v1ing you will be VERY difficult, so buy some wards as you push so you can leave if people come to gank you in numbers. You WILL be focused if you have been doing your job, so about now you should start buying some tankier items like Force of Nature, Randuin's Omen, or Guardian Angel. If you have been receiving little or no focus for some reason, or are simply too fed to be killed in fights, go ahead and buy an Abyssal Mask to become completely unstoppable.