Really interesting idea, if it could work out, it would assure that 100% of all submitted in-game reports would be looked at which is of course great.
However, that would also make the need for admin presence in-game much smaller, as all reports would then be relocated to the website. An admin could then technically not even have the game(s) at all, and just operate on the website. The interesting bit is that the whole concept of having admins in-game would have an alternative, which then brings up questions about wether it's actually needed for report claiming 'there' when you can do it 'here'.
Of course, there will always occur situations where action is needed right away (CB abuse, blocking, spam, etc.), so that's always a reason to have people in-game to deal with reports. And to add on your suggested function, it could make so that all dismissed in-game reports (non-claimed) will get uploaded to the web, instead of all the reports (if that was your intended thought). But still a really interesting topic which I think will bring up new discussable topics.