Below are my comments about what I think was a related question:
I think both M-x shell-command and M-x compile execute commands in an inferior shell via call-process. Try the following in your .emacs (or just evaluate):
(setq shell-file-name "bash")
(setq shell-command-switch "-ic")
I notice that after evaluation of the above, .bashrc aliases are picked up for use by both M-x shell-command and M-x compile, i.e
M-x compile RET your_alias RET
should then work.
My environment: Emacs 24.1 (pretest rc1), OSX 10.7.3