I agree that there could be some improvement in the difference in color between checked and unchecked. A slightly more greener "checked" checkmark or a slightly lighter gray "unchecked" checkmark would solve this.
But at the same time, all of the other buttons on the site that indicate "clicked or not" start out gray as well, and change into a colored version when clicked. This by itself is a clear and consistent indication.
Here they are side by side. Take note of the gray-to-colored indication in the voting buttons as well:
Lastly, keep in mind that only the questioner will see any "unchecked" checkmarks. If there are multiple answers provided to the question, they would all appear gray at first, and obviously only one of them can be selected as correct.
Here's a crude mspaint mockup for your suggestion. I have to say, I like it better than the darker checkmark.