OOoh, this is one that I could answer at great, boring length, or give a short version. I'll try for the latter.
The utility of cochlear implants varies greatly. In even the best-case scenario, though, they don't work like glasses, a perfect correction to the sensory deficit. A deaf person who gets cochlear implants does not become hearing.
So, with that as a starting point, there's a wide range of how much useful hearing someone gains with a cochlear implant. And "useful" is really the rub. They're VERY good at indicating a sound has occurred, and so they tend to do great in audiograms -- click the button when you hear a sound. The problem, though, is whether that translates to being able to carry on a conversation or generally interact with the world.
I have many deaf friends with cochlear implants who continue to use ASL, interpreters, etc., but enjoy having a little more data; one friend of mine says it's great to be able to tell when a car is coming when she's about to cross the street, for example. I have met many (MANY) (MANY
) people who expected to be able to hear enough to function with their cochlear implants, and who were sorely disappointed. (To the point of being clinically depressed.)
And this isn't going into all the people I know who got CIs and then had terrible side effects; one friend had terrible vertigo for over a year (still has it but less frequently), which meant she had to miss a lot of work and couldn't pick up her toddler twins.
A typical "success story" is this one from someone I met who went on at great length about how much she loved them (in ASL, at a deaf event). Her husband is hearing, and one morning she woke up, put on her CIs, and heard some incredible racket. Some sort of mechanical grating noise, super-loud, really alarming. She woke up her husband and he said he couldn't hear anything. She persisted, and they finally figured out -- oh, she could hear birds! That was the horrible, grating, awful sound.