Usually if children are implanted at an early age, they greater chance for success with spoken language. This is because the brain is still developing and absorbing new stimuli and making sense of what it means. I don't agree that learning ASL will be a detriment to language development. After all, hearing parents of hearing kids are teaching them "baby signs".
Talking Hands is correct when she says they are still deaf or hard of hearing. You should still employ good communication strategies with them (look at them when talking to them, make sure your face is visible, good lighting, etc.). Parents sometimes think CIs are a "cure" or a "quick fix" to make their kids "normal". This is absolutely false. Even those "success stories" invested lots of time and work in speech and auditory training.
My sincere apologies for all the quotation marks.