Omnidirectional departure procedures simply means that someone has taken the time to check the obstacles all round the departure aerodrome rather than simply along the defined track in the case of a SID. Just like on a SID, if the standard climb gradient does not acheive the required obstacle clearance the the gradient is increased or other restrictions are put in place.
As far as separation is concerned, that is a separate issue as is obstacle clearance in the event of an engine failure.