So after several games playing gangplank with manamura, I can safely say this:
Its an amazing item to get on your second back, however you have to live after your first back without sheen (unless you are very ahead for some reason) which is difficult to say the least.
However, it provides a few things: Once you actually get manamura, it nearly doubles your AD, from 80ish base at level 6-7, to 150+ if you have good stacks and your manaflow band. On top of that fact is that people who know the GP matchup know it based around sheen, so it also messes with their matchup knowledge a fair bit, as the way you play GP with manamura in lane is exceptionally different, basing most of lane around shoving in waves rather than controlling them, and using your barrels to poke rather than your Q. I dont think this would work if they didnt recently buff the damage GP barrels did to champions early game (It went from 30 bonus damage at first rank to like 80).
Apart from that, its a good pick for late game if you got it stacked early, but not something so amazing that it sets it appart from his other options. Like lane, having a manamura and trinity force turns your late game the opposite way (if you are building damage at least) You go from Hitting the enemy team with a huge barrel combo, to a poke and 1v1 focused style. Its like playing a hybrid of Ezreal and irelia. You keep your distance and poke them, but if they try to move in on you, not only can you kite with barrels, but your melee is actually even scarier than your Q.
All in all, I think I will start using Manamura if I am ahead in the early game, as it pushes me even further ahead (I view it kind of like a soulstealer but for AD) but it is definitely not a must-pick, especially for crit or tank builds, but the fact that it opens up an entirely new playstyle on him, one that other people arent familiar with and dont know how to deal with too well, is the main selling point for this.
Here is one good example of the power of this build. I was 2/3/7, and decent CS, so a good lane but I was by no means fed.
It does work well against tanks, however, since you can build cleaver and a pen item, along with trinity and manamura, and its hard for tanks to do much against it.
This is where the build shines the most. Aside from Nidalee soaking up Rengar's jump, she really didnt do anything here, so I was basically 1v3, killed two of them, and almost killed rakan, whilst forcing out his flash.
I had manamura into IBG, was somewhat fed (and VERY fed after this lmao).
The simple fact of the build is that enemies cannot wait for you to make a mistake, like a lot of fights in mid-highish elo happen.
The enemy has to engage on you immediately and kill you right then (Which is tough considering that GP can reach 100 armor and MR with no defensive items) or run away, since any time spent fighting him, even at long range, he is quickly draining your health.
the rundown of ideal situations for the different GP builds:
Damage: Teamfight, enemy team clumped up
Tank: 1v1 fights (split pushing) and short skirmishes
Manamura: Small skirmishes (not full teamfights, but not 1v1s either, so like 2v2s and such)
cause the fault that a lot of people make is that if you build damage GP, you play him like an ADC that just has an AOE, which is wrong. Damage GP is an artillery mage, very similar to syndra.
this build is the true ADC playstyle, where its best to have someone else backing you up. While you may be able to put out damage, you can still be deleted pretty fast if you dont have any defensive items. Whereas full damage GP, your defense is your damage. You can pretty much crit barrel+melee attack and kill any squishy in the game, so you dont need to worry about being jumped on. This GP just wants to be able to take down targets one at a time, quickly burning through one and using barrels to keep the others at bay, and when he is done with one, he moves on to the next.