The purpose of check box is to select an option, as being experienced by all in internet. If you alter this default fuctionality, your users will find it different from what they are familiar with.
However if you have multiple options against same document such as Open, Edit, Delete etc then it’s fine. Once again, when only one option is valid, you should go for radio button instead of check box.
For implementing this add a formula in a view column which gives following value when computed:
That was just a hint… there might be a errors in that. I haven’t checked this code.