This is just my impression, from having worked with C2 for a while.
If you only use the standard plugins in C2, it would be quite hard to make a simple DAW.
The built-in features of C2 work very well for games and even a lot of applications, but many of the core features of a DAW are not natively supported by C2, and might be pretty hard to implement.
C2 is very flexible though. Using the SDK, you can build custom plugins to handle just about anything.
Just about everything involving audio, midi, and VST style modules would need to be implemented as custom plugins. The built-in Audio plugin, is pretty nice, and solves a lot of tricky web audio problems, but it's focus is fundamentally not tailored to DAW tasks. I think you'd only be able to use it for UI sounds in this case.
So, I would probably not recommend building a DAW as your first major project in C2.