Most *.nds files will run, yes, unless they require GBA compatibility. The only real program I can think of that does this is SnezziDS. Also note that older pre-DLDI homebrew that accesses the filesystem will most likely not work on an R4. Anything with DLDI support however should work fine.
The latest R4 firmware has a DLDI autopatcher, so you don't need to patch on the computer.
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