No, it wouldn't. It doesn't have a Dreamcast connector. This box actually converts the signal to VGA, whereas the Dreamcast natively supports VGA.
The VGA cables and boxes for DC don't do anything extra. The cable will provide monitor and audio hookup, while boxes like the Naki VGA box provide monitor hookup, audio hookup, and S-Vid and composite hookups for running out to a TV. Not all games support VGA, though there's ways around it. The results with those games which do support it range from "blech" to "HOLY #@%$!!!" For example, pretty much most 3D games that support it will benefit. The recent crop of 2D-style, 3D-based shmups look incredible. Capcom Vs. SNK is a mixed bag. Pre-fight pics are anti-aliased to hell and sprites don't look all that great. I think backgrounds looked good though (it's been a while since I gave it a go). Colors really popped through VGA though.
If you can find one, I'd recommend the Naki box. The only problem with it is that it doesn't provide for VGA passthrough, meaning you'll have to unhook it every time you want to hook your PC to the monitor, unless you use a switchbox or y-cable. Function-wise, though, it's great.
If you're looking for something that'll provide passthrough and just convert standard S-Vid and/or composite from up to 5 consoles, there's other options on the market. Just look for a universal VGA box.