Logic would state that yes, the average citizen knew that many stormtroopers were* clones.
*Exactly what percentage of current Stormtroopers were clones after The Empire was officially formed is up for discussion.
Consider the fact that there was a huge conflict actually called "The Clone War".
Dubbed this by Yoda at the Battle of Geonosis,
"Victory? Victory, you say? Master Obi-Wan, not victory. The shroud of the dark side has fallen. Begun, the Clone War has." -Yoda
The war was named after the clone troopers utilized by the Republic against the battle droid forces of the Separatists. These armies, the Grand Army of the Republic and the Separatist Droid Army, were two of the largest ever pitted against each other in galactic history, and the fighting between them rapidly spread to countless inhabited worlds.
This was not some small skirmish in a remote area. It spanned across the galaxy. Those who were not involved were surely at least aware of it. Even if one was not aware of the specifics of the war, the name of it is sort of a dead giveaway that clones are somehow involved.
That's well and good, but what about 20 years later? Even The Force has largely faded into obscurity.
Even Luke, who lives on the planet furthest away from the bright center of the universe, knows of The Clone Wars.
From the script:
BEN: That's what your uncle told you. He didn't hold with your
father's ideals. Thought he should have stayed here and not gotten
LUKE: You fought in the Clone Wars?
BEN: Yes, I was once a Jedi Knight the same as your father.
So, sticking with G-Canon - while not 100% positively affirming it, there is enough evidence to fairly assume that the average citizen knew that Stormtroopers were clones.