There are two bars. One for being illegal, and one for being deported. He doesn't have one for being deported because he got voluntary departure, but he may still be subject to the 3 or 10 year bars, depending on how much time he was illegal inside the U.S. (10 years if he had more than 1 year of being illegal).
You can't find out because no one can tell you for sure, not even the officer that will be in charge of his file. Why is this? Because the officer has to sit down with EVERYTHING and has to look through everything and has to weigh all the pros and cons of letting him back into the U.S. and not until the officer does this will a definite decision be made. So how can anyone know beforehand if someone has a 100% chance of approval or denial? They really can't. And as to how long it will take, that I can give you a rough estimate like I did before based upon what I have seen, 6 months to a year or so.
Now I understand the news is not good, but please don't shoot the messenger. I can explain to you why it is so difficult. You see, the U.S. doesn't want to #1) reward immigration violators just because they were able to elude capture or whatever long enough to find someone to marry and have kids in the U.S., and #2) to send the message to potential future violators that if they do this, meaning violate the border and laws, hide out long enough to find a U.S. Citizen to marry and have kids, that it is easy to get a waiver (forgiveness) to come back in.
Imagine if they did send that message? We could have many more millions of violators trying to get into the country. I know that this doesn't help your situation, but I am just trying to explain their mentality.
The lucky thing is that they understand that there are some extreme humanitarian cases and this is why there exist some waivers available. The problem is that they aren't easy to get, not should they be easy to get. This is why they usually only approve them in, as I said, extreme humanitarian situations.