I connected Battery + not to the harness that plugs into CMP, but directly to the CMP sensor pin. By doing so could I still somehow powered up something else that lead my car to suddenly start?

I think your theory about pull up resistor "providing" those 2.5V with EMS2 fuse removed could make sense (at least there *was* continuity from EMS2 branch to the one of the PCM pins). In that case I may indeed be focusing on the wrong thing. Though why GM designed circuit in such way - what's the purpose of such circuit besides monitoring healthiness of EMS2 fuse and Main relay? I think it would still be great if some forum members with the same 2007 Aveo Notchback could double confirm this for me to clear any remaining doubt.

Assuming that those 2.5V are expected, then I may have to fall back to the theory where Main Relay was faulty, because:
1. when car did not start the voltage on EMS2 branch slowly grew from 2.5V to 12V. And at the time of cranking again fell from 12V to ~2.5V.
2. when car started, perhaps, main relay opened up completely. Though, not sure how likely it is for relay to be broken in a such way.

Maybe I should try to reproduce this issue again and then try to swap main relay to see if it solved the issue?