Yes, but you need a special server for this. I think they're pretty expensive. The server from the company where I work has that feature and we're paying 350 $/year.
You dont need a "special server" just enter the domain like you have done. The only thing is it may need some configuration, for example if you have cpanel you have to add the ip your connecting from to the access list, in order to access the database.
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Well, I got told that most servers don't support external database access. Would be good they would though, this way we wouldn't have to pay 350 $ for it.