In ArcExplorer, I'm wondering if you can connect to a non-SDE database, like SQL Server, with geometry or geography columns?
You can download a data expansion pack (if that's the correct term) that will allow you to connect to SQL/SDE geodatabases. Remember SDE sits on a database and adds extra functionality (or overhead). At ArcGIS 10.1 data uses SQL geometry or geography natively, so a SQL connection to spatial data should work. You'll also have to make sure your client computer has the correct SQL native client installed. And use the direct connect method for your connection.