Unfortunately not. The SiteIsOffline flag is checked in our URL processing engine and is run for all requests that are in "LiveSite" ViewMode. You can technically access the page in edit mode (?viewmode=18), but this is also a very different view from the live site.
You could consider altering your web parts to operate as expected in Preview mode, or you could take a backup of the site and run it locally where you can put it "online" and view the live changes.