My opinion is if you have got: A) NO SID from ATC or the Airport you operate out of has no specific SID, and say it is night and the weather isn't the prettiest in my opinion it would be prudent to fly your companys engine out escape route or the normal engine escape route for example this airport in Australia has no SID or STARS but the airline requires off Rwy 18 that the crews use the ALL ENGINES OPERATING procedures to depart the strip. It is like the saying if you have a GPS/GPWS and switch it off in the flightdeck, you are not using your resources at 100%
AIRPORT: MAROOCHYDORE
RUNWAY: 18
ENGINE FAILURE AT OR AFTER V1
1. Standard procedures following engine failure at or after V1.
2. Track 184°M.
3. At 2 DME turn LEFT track 090°M.
4. Acceleration altitude 800 ft QNH.
5. VMC Visual circuit and landing.
....IMC Continue climb and proceeds for an instrument approach.
...OR
...Continue climb in an appropriate holding pattern to lowest safe altitude for departure track.
ALL ENGINES OPERATING
1. After leaving 500 ft QNH proceed to intercept departure track.