Technically, if you're sending your character into a predicted and essentially guaranteed death, you're not encountering a "chance" of failure in the sense that I suspect you mean. What you're doing is quite scripted. And if your actual goal was to die nobly in battle, then you haven't "failed" in any meaningful sense of the term. So... in terms of encountering a "chance of failure," a character who intentionally goes to a guaranteed doom is encountering exactly as much "chance of failure" as a character who stays safely at home. Both characters are doing what they intended and accomplishing what they planned, and neither has an appreciable chance of not accomplishing their intended ends.
As for the general issue... I feel like "chance of failure" gets abused as a phrase. There's really two ways of using it.
The first would be, "If I make the right decisions or perform the right actions I will succeed, but If I am wrong I will fail. There is a chance that I will not be wise enough to make good decisions or perform the correct actions, therefore there is a chance I will fail."
The second is, "Even if I make the right decisions, there is a real world chance that I will fail. Given enough trials, eventually I will fail even though I made wise decisions."
To give an example, suppose I am playing a card game of deduction in which I need to figure out what card you are holding. I decide that if my reasoning is correct then it is absolutely 100% certain that you are holding an Ace of Clubs. I guess Ace of Clubs. At this point there is a chance that my impressions regarding my reasoning are incorrect, and that I have reasoned improperly. If so, I will lose. This is a "chance of failure" in the first sense.
Now imagine a second game, perhaps a wargame. I have successfully outmaneuvered your forces with my own, and now our troops will exchange fire. I have bonus modifiers for high ground, for protective embankments, for enfilading you, for having air support, and for having a secure supply line. In fact, I have all possible bonuses in the entire game. With all of my modifiers in place, I need to roll at least a 3 in a 2d6 in order to win. This is a "chance of failure" in the second sense, because even though I have done literally everything possible to ensure my success, I still might roll a 2.
I tend to prefer the first sense in which I've defined the phrase.
Random factors push you towards the second sense of the phrase, but they don't guarantee that it's dominant. One way random factors can help the first sense of "chance of failure" is by randomizing events so that you have to adjust tactics and react to unexpected advantages and setbacks. In general, a high random factor pushes you towards the second sense of "chance of danger." 4e seems to be designed to have a relatively high random factor on individual attacks, but to require a series of them during which you will see highs and lows. Your character is then provided with certain remedial measures to take when the lows start to dominate, such as using second wind or rare powers. This interplay is generally called "strategy." And just as a high random factor can enhance the second sense of the phrase "chance of failure," the type of strategy I've outlined can enhance the first.