No probs. See attached. Ive used them on ICS MIUI 4.0.4 and ICS 4.0.3
Doesnt hurt to try, if it works, cant take credit, downloaded these 2 apk's from somewhere in this thread.
Backup existing email and exchange apks from system/app then delete them and reboot
copy new email and exchange apks into system/app and change permissions for both owner (read/write) and others to read only then reboot
then begin to setup your email and when complete and it asks you for security, select yes, choose your relevant options but when asked to select activate, reboot again.
Then load email again and this time hopefully you wont be asked for a pswd etc and it will start to sync.
Hope it works for you, let us know if it does.