The transfer speed would be a problem, yes. If my experiences with DSLinux are any indication, the DS can actually receive data quite fast (80-100 kb/s), but once it starts writing that data to the card itself, things really bog down to about 30 kb/s max.
In addition to the Lilou Combox app, you could try the various networking apps available in DSLinux if you have a slot-2 device with extra RAM. There's ftpd for FTP transfers, and Samba support for using a standard networking client, plus you might be able to use ssh or wget for something as well.