You're not really sleeping if you're using alcohol, you're passing out. And possibly have to take a shot in the middle of the night. Alcohol is a lousy sleep agent. It's very short acting and completely destroys your sleep architecture.
I was cross-addicted to sleeping pills (lunesta, the green butterfly thingie). So when I detoxed, they switched me to valium for the alcohol and simultaneously tapered the lunesta. My insomnia wasn't bad in the acute stages, but lingered on for a few weeks in decreasing severity.
Man, when you DO finally sleep when you're not drinking you feel so much more refreshed. Because real sleep.