* DISCLAIMER: MY ADVICE IS FOR GUIDANCE ONLY AND MAY BE COMPLETELY WRONG *
In the event of an engine failure, you either fly the SID, or the published engine out SID (if one exists).
Beyond that, whilst having a pre-briefed way out is an excellent idea, and helps with situational awareness by making you aware of things such as terrain before you take off, my personal opinion is that do whatever is necessary to keep the thing flying!
As was said above - if you're flying a twin that is only going down on one engine, well, the brown stuff has hit the fan and there is sod all anyone can do about it. Just hope that you can walk away from it.
Personally, I'd throw the book out the window and just fly the thing out of trouble (assuming it climbs). If I survived long enough to face an inquiry about it afterwards, I'd be quite happy.
Flying a SID or EO procedure would be amongst the last things on my mind.
Don't forget to fly the aircraft!
It seems to be a basic error made over and over again.
ECAM Actions.