Er, I had surgery yesterday, and I'm on some strong medication at the moment, so what I'm about to say may contain more flaws than usual
I was born and grew up with better hearing than most people tested at the age I was originally tested in first or second grade, don't remember which. Anyway, I began losing my hearing at around age 20, and as of this summer, I was told that I have absolutely no residual hearing.
Jeez, I think I'm about to pass out. Well, let me see if I can finish this thought.
My mom and my sister have told me that my speech is exactly the same as when I was hearing, although I did have a little speech therapy earlier, which may have given me an advantage over those who haven't.
There are times, however, when I cannot figure out what word to say, and I must sign it. If I were signing ASL, there are vast amounts of concepts that are expressed in ASL in such a way as to be impossible to duplicate in voice, and I mean IMPOSSIBLE. You can have an IQ of 10,000 and it will be impossible. It has nothing to do with skill. The basic principals of the language of ASL are entirely different from all spoken languages.
However, because my family originally agreed to learn SEE, I reluctantly ordered a SEE dictionary and studied and learned SEE so that I could communicate with them. I very quickly became fluent since SEE is an exact copy of my native language of English. My mom wanted me to speak while I signed because she believed that she would learn more quickly that way. However, though I can speak very well and I can sign in SEE very well, when I try to do both at once, they both simultaneously suffer tremendously. I know there are people who can speak and sign at the same time, but they are not speaking English while signing ASL. In all likelihood, they're signing PSE or SEE.
I did have a deaf ASL instructor who spoke when he signed, but he was not speaking English. He only spoke in ASL word order, and always left out concepts that couldn't be translated directly into English. He did this only for the first few weeks of the class, and after that, speaking was forbidden. The advantage I got out of the rule against speaking was actually that it encouraged us to learn ASL much more quickly due to it being our only form of communication combined with our need to communicate. It doesn't mean you can't speak out in the real world, but it's a very useful and effective educational tool.
Now, with my limited experience with ASL, I feel I should point out that from what I've seen, I wouldn't recommend speaking while signing ASL because for one thing, it doesn't make sense, and for another thing, not speaking allows you to use more facial expressions to emphasise what you're signing. Besides, as many have pointed out, it's not the same language, so it's silly to speak two languages at once, even if you have a duel-core processor in your brain that allows you do that.
This is my personal viewpoint and experiences, granted I've expressed them while under the influence of a potent pain medication due to my recent surgery yesterday