Yes, this is what I meant. By "disconnected" I meant causally disconnected, i.e. spacelike separated. Sorry for not making that clearer!
And yes, you can always boost to a frame such that the "order" of spacelike separated events will change (i.e., reverse which event is above and which is below a line of simultaneity). Since you can't objectively say which event happened first, they must be unable to influence each other, hence "causally disconnected".
And yes, you can always boost to a frame such that the "order" of spacelike separated events will change (i.e., reverse which event is above and which is below a line of simultaneity). Since you can't objectively say which event happened first, they must be unable to influence each other, hence "causally disconnected".