Some people have managed to get a drivers license while keeping their old one but it depends on how good you are at begging and how nice is the person you are dealing with but it is true that they aren't actually supposed to let you keep both licenses. What some people have done is after giving up their license and getting a Canadian one, they go back to old country and get their license re-issued there. Old country might not care if you have two licenses or maybe they just tell them they lost the old one.
Like qorax said, you could actually go through the graduated licensing system without telling them you have a US license in which case they would not know to ask for it. This would work really well if you are not moving right away because you could take the written exam on your first trip, then go a year later and take the basic road test and then you are allowed to drive.
However, since it is still against the rules to have two licenses, if you are pulled over by the police and they happen to see both of them, they will most likely take one.