You don't see turtle pellets floating around in a pond either.
I've given my turts bits of hard-boiled egg whites (not the yolks) on occasion when they were hatchlings. As part of the overall diet, it's OK to do so. The whites are pure protein, however, so if you wanted to offer some, it should be done sparingly and rarely. I don't mash--I cut a few thin slices to look like worms.
I use organic eggs, but don't use the shell, although some people do grind them up for use as a calcium supplement (you can boil the shell to soften it). With regular eggs, I've read there is the question of the hormones they contain.
"You become responsible, forever, for what you have tamed." -Antoine de Saint Exupery-