not exacly, you can pass there NodeGUID which is better than NodeID.
You can achive that my overriding the default extender ContentEditTabsControlExtender located in /App_Code/CMSModules/Content/Extenders/ContentEditTabsControlExtender.cs which is assigned as tab exntender in Edit ui element of Pages. You need to change one line of method OnTabCreated:
tab.RedirectUrl = DocumentUIHelper.GetDocumentPageUrl(settings);
and replace it with
tab.RedirectUrl = URLHelper.AddParameterToUrl(DocumentUIHelper.GetDocumentPageUrl(settings), "nodeguid", Node.NodeGUID.ToString());
It's not good to modify system files, but... you know ;)