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In a very general sense there is nothing inherently wrong with using an icon to indicate some binary state (for instance visible/not visible for a page in a CMS), provided the implementation is sound. But the fact that you're suggesting that these icons could be substituted for checkboxes in 'edit mode' does rather suggest that they would represent the same ...

When designing an interface, you should focus on making it as easy to use as you can, not on doing something new for the sake of it. And as your question stands you haven't really shown what the problem with checkboxes is that you are going to solve with icons and colours. So breaking it down with specific reasons: Checkboxes clearly indicate their state ...