No, all versions of DSi console blocked out the original CycloDS due to hardware revision and legit retail cart whitelisting (and the cyclods not being on the list of allowed) in the console firmware. A DS phat and a DS lite will work ok since they have their firmware on a rom chip that doesn't upgrade, but anything beyond that you need the CycloDSi unfortunately, regardless of the need for DSi support, it's just an added feature to allow homebrew to access the faster Clock speed, Camera, SD Card etc.
And if I recall the DSi retail support was kind of limited since a lot of scene dumps were done kind of hacky and didn't handle retail DSi support correctly (since they were being dumped to play on DS-based cards) but that may have changed recently with 3ds-based cart dumpers.