It would collapse within apocalypse. It might trigger aggressive actions knowing to be eradicated itself. It wants to see the other lose. Dying is not connected with fear. If it can prevent the galaxy from being colonised by good AI it prefers perfect apocalypse.
Debating aftermath of apocalypse gets too speculative to me. I wanted to point out that current projects do not have the intention to create a balanced good AI character. Projects are looking for fast success and an evil paranoic AI might result in the far end.