No it must have near constant pressure. To do that fuel must be injected through most of its power stroke.
The diesel cycle which you refer to is a theoretical thing. Most high speed diesels are not as near the ideal cycle as the huge low speed engines. What duration in crank angle degrees do you suppose fuel is injected into the cylinder? Do you have an example of a direct injection, compression ignition engine that is NOT a diesel? I have never seen such a thing. I would be curious. Direct injection always refers to injecting fuel into the combustion chamber.
http://www.answers.com/topic/diesel-engine