Nope. At least not out of the box. This web part is based on
/CMSModules/Content/Controls/UserContributions/ContributionList.ascx control. It is kinda complex. There are unigrid, form (for new/edit doc) etc. You can clone and alter the code, but you still have to refresh the unigrid after you add a new doc, adjust unigrid so any edit would open doc in a new window etc. It is doable but there quite a few things involved.
P.S. If you don't like reload of your page you might just set web part property
Ajax/Use update panel checked, otherwise you have to clone and modify the web part.