Borderlands – Does Deathtrap get the Shock Damage boosts

As you said, these are all the pieces already. If what I'd figure is your question it's easy to answer: "How much damage would I do if I fire for $Length time?"

$Length * $RoF = X rounds
X rounds * $damage = gunDamage
X rounds * $DOT% = avgDotAmount

DoTs are smart in this game, they all have their separate timers and can stack independently from one another. This makes the damage as intuitive as possible:

dotDamage = avgDotAmount * ticks(element)
totalDamage = (gunDamage + dotDamage) * multiplier(element)

As this was far too easy to answer, I can only assume your question would be like
"When can I stop firing, knowing that my DoTs will kill the enemy?" To which the answer would be "Never, unless the target isn't currently affected, then keep firing."

To us human player at least; for all the data is there in the fountain of numbers that spew from the target you are perforating with bullets. Would we be perfect computers, we could see when a new dot starts ticking(it wouldn't have a previous tick before it) and thus know exactly how many ticks are left. Being human, all we can say is "it's on fire" or "it's not on fire." This makes knowing for SURE your target is going to die impossible, the best one could do is make a normal distribution graph(wiki) with the probabilities if your target will die.

If that's really what you'd want, I could run it through some model, but it's still gonna be a pretty useless graph. Input the specific gun and skills you're using, and you could get a graph with probabilities mapped vs dotDamage. Even if you could watch that while shooting things, you can only guess how much health your target has left.

If instead, and my final guess, the question would be "How much do I overkill?" that amounts to the same, as that is also "Amount of dotDamage still to be done."

Playing Gaige in a "no aiming" style requires a different mindset from the other Vault Hunters. The Ordered Chaos tree works better when using a weapon with a low Magazine Size but high Reload Rate. Generally, that means you're shifting away from automatic weapons such as SMGs and Assault Rifles that often have Magazine Sizes of 20-30+.

One other thing you'll need to force yourself to forget is reloading in between fights. Anarchy stacks based on emptying your magazine or killing an enemy, so the fewer shots you have your current magazine, the sooner you'll accumulate stacks of Anarchy.

Anarchy itself is an odd mechanic. Because it reduces Accuracy per stack, you'll actually want to use a weapon with a decent amount of Accuracy otherwise you'll be doing little damage even at close range (a la Sledge's Shotgun from the first Borderlands). Combined with the need for low Magazine Size and high Reload Rate, your best shot for a go-to weapon is anything from the pistol family. Be a revolver or a repeater, these guns have respectable Accuracy and Fire Rate, without having the relatively high Magazine Sizes you want to avoid.

With this mind, you can stack Anarchy as quickly as possible for use with your other skills. While this isn't so much a "no aiming" style, Gaige's Ordered Chaos tree puts a lower emphasis on aiming than other playstyles. What's making this hard to swallow isn't so much the skill build but the mindset involved. A lot of it run counters to what you learned in other FPSs.

P.S. If you really want tips for skill builds, I would recommend getting the Close Enough skill in the Best Friends Forever tree as soon as you invest a couple of points in the Ordered Chaos tree. With your decreased Accuracy from Anarchy stacks, the ricochet will definitely help. After more points in the Ordered Chaos tree, I would recommend coming back to the Best Friends Forever tree for The Better Half skill. As you want to empty your magazines as quickly as possible, any source of increased Fire Rate helps. In fact, The Better Half skill might actually make high Magazine Size weapons such as Assault Rifles, Machineguns, and SMGs more palatable to use.