I will try and perform a test of that to reveal the result for you. Guessing , based on my previous experience in other applications, would be that the Eneloop would just cut off. No, the M31 module wont fit into the Elite heads but I can attest that it will fit the Malkoff VME Valiant Concepts Head. I run that setup in a twisty 2xAA Valiant Concepts body or the Maxlight Extreme 1xAA body previously mentioned. Nice and compact and ~ 115lumens.
I wonder if the m31 would fit the new c2e head from lumens factory