It would be great if, an addition to choosing one of the built-in effects, I could also choose a from a few simple built-in drum machine rhythms which would also play through the guitar and mix with the guitar sound.
using MIDI programs on my phone and computer, I have experimented with sending drum sounds through the TWA, some work really well but the key is to Keep it Simple, and don't use to much low end (e.g. Toms and Kick Drum) in the mix or it sounds super muddy.
Some Cajons may be a little thick to drive, but reverb and delay will usually work okay. May be a bit tricky as far as mounting goes, but it can be done.
I certainly don't see why not! It would be a matter of making sure the surface the TWA is to connect with would be thin enough to drive adequately.