May be its just me, but I think there is a very remote possibility they will do such a check. Truth is there is nothing wrong with your file. So, I think its better to keep it clean that way. Saying something like "I didn't live with a guy whom I'm not seeing now, long long ago" is attracting unnecessary attention and will only delay the file, raise red flags. They may start to think "hmmmm, why did she take the time to mention something about it, if there is nothing there. There must be something there "