You would not know if a name was suggested to a CH already. But, you will know if they CH imported your name into the contest and I imagine it will look just like if you did it yourself. If the CH accidentally tried to import the same name, I am guessing that the system would tell them the name is already in their contest and if it turns out that is not true, then we should report that to SH to fix. They are great about fixing glitches and that would be a glitch because I'm sure they don't want that to happen either.
There are two different things: The suggestion list and the names the CH actually imports. We don't know when our name has been suggested and the CH passes it by. So, we would still be able to enter the name because the CH hasn't imported it.
My suggestion would be for creatives to try it and help SH work out any glitches.