Sadly not. Nintendo has also confirmed that points will not be transferable between the two platforms. So if you register 1000 points on your Wii and spend 500 of them, you can’t then buy something for 500 points on the DSi Store – despite the fact that it’s very likely that you’ll have registered both machines using the same ‘Club Nintendo’ account. Boo.
This strikes us a very dumb move on Nintendo’s part. If you find yourself in the position of wanting a game on WiiWare and DS Ware, you might have to purchase TWO cards to get them, even though one card could potentially grant enough points for both titles.