The GBA contained a GB/C CPU for backwards compatibility, but it was not used by GBA games.
When the DS came out, it removed this CPU.
Technically not quite true, there are a few GBA games that use the GB compatibility chip for music, Street fighter Alpha 3 at least did, to save rom space.
For someone with a DSTwo or other DS mode flash cart, I recommend the GBARunner2. It's "a GBA hypervisor for DS. (like Nintendont for GC on Wii)". It can't save yet, but it has been running most games in playable states.
https://gbatemp.net/threads/gbarunner2.451970/
https://github.com/Gericom/GBARunner2