DLDI itself doesn't bother about the file system. It only acts as a block driver, one layer below. It might not be able to work on media with more than 4GB or that use exotic partitioning scheme.
libfat is the component that would need specific support for EXFAT. But even if latest version of libfat do support it (e.g. thanks to wii port), all homebrew would have to be updated -- I mean recompiled and linked against the new version -- to work on a EXFAT device. Needless to say that this is unlikely to happen and that you'd better format your media as FAT if you intend to use it for NDS homebrews.
Oh, and on most linkers, that would require a firmware upgrade because the linker use the SD card to store files of its own, too. again, this might not be available except you have a fresh new linker.