I think I see what you're asking - you're trying to see if your Wii can act as a router if you were to use the USB -> ethernet adaptor and plug it into your modem.
I'm pretty sure the answer is No.
Of course, if you're using the WiFi to connect your Wii to a wireless router, your DS would be able to get online through your router, but (most likely) not through the Wii.
Broadband meaning DSL or Cable, you would still have to have an incoming line going through a DSL or Cable modem. Then you can connect it to anything with a NIC. But the whole "convert broadband to wifi" thing doesn't really make any sense.
