I'm a bit late to this party, but here's some info.
A dual-link DVI connector is not designed for driving dual monitors; it is designed to supply the extra bandwidth and signaling required for high resolution. DVI splitters work by literally splitting the signal and routing the signals so that one monitor actually communicates with the video card while the other monitor simply receives the signal from the video card. One thing to keep in mind is that there is not standard specification for a DVI splitter, so whether or not your video card will work with a splitter is rather variable....it's mostly luck of the draw.
To muddy the waters even more, there's a port that does support dual monitor output in a single connector. It actually looks very similar to a DVI port, except it's missing the "blade" at one end of the connector. It's called the DMS-59 connector and electrically it contains two single-link DVI connections along with two VGA connections. Computers/video cards that have this port generally come with adapters that split out to two connectors.
Picture for reference:
DMS-59
Dual-link DVI
I have heard that splitters don't work as well with single link DVI ports, I would assume that's because of the reduced signaling.