I think it's likely to do that because any unbounded goal that doesn't explicitly protect biological life (and we have no idea how to actually define such a stipulation) is best solved by killing all biological life. This is an obvious consequence of unbounded goals consuming unbounded resources, conflicting with biological life needing resources to sustain itself.
>how do you think it's going to happen?
I can speculate (e.g. we're nowhere close to the maximum killing power of drones), but I don't know because I only have human intelligence. An ASI is by definition smarter than me and surely capable of coming up with better ideas. But I do know that it's not going to do anything that would make a good sci-fi plot, because those always give the humans a chance to win, which would be stupid. Everything will seem to be going great and then everybody suddenly and unexpectedly dies.