Yes you can, but it's a royal pain. Most
jdbc drivers use a tcp/ip channel to the database server such as SQL Server's 1433 or PostgreSQL's port 5432. Thus, in addition to having to sign the applet (painful enough), you also have to be sure that there will be no firewalls choking off the stream.
Usually it's just easier to do an n-tier solution and use http tunnelling between the applet and a
servlet or
JSP which does the actual database work.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.