Hi Ami M,
Not through AdWords or Analytics. It's possible you could find that data in your web logs.
If you are trying to identify AdWords conversions by customer you'll need some sort of tracking system. I look for the presence of a gclid value in the query string when the user first hits the site. If I find one, I set a cookie I can read later. When a conversion happens, I look for that cookie. If it exists, I assign that conversion AdWords source.
Best of Luck!