I'm excited to share that I've got async evaluation working (crudely) with ob-shell.  A rough implementation is attached.  

It has clear issues, such as the prompt being present in the output:

#+begin_src sh :session tester :async t
echo "By sending delimiters separately..."
sleep 3
slep 1
echo "typos don't cause problems--^"
#+end_src

#+RESULTS:
: org_babel_sh_prompt> By sending delimiters separately...
: org_babel_sh_prompt> org_babel_sh_prompt> sh: slep: command not found
: org_babel_sh_prompt> typos don't cause problems--^
: org_babel_sh_prompt>

It's not clear to me if that's something that a better regexp would handle or if it should be cleaned up in the callback function.  I'm still figuring out how it's done in ob-python and ob-R.

Any feedback or advice is welcome.