If there really is a danger with terrain the emergency turn procedures normally cater for it.
Perhaps ... but, then again, more likely, probably not .. beyond the normal routine OEI failure. Highly dependent on the operator's integrity and the Regulator's oversight and technical competence re OEI escape planning.
avoid terrain using the terrain function
That's fine if there's one gynormous hill in an otherwise flat landscape .. the reality is that a pilot-interpreted radar image is of considerably less use than the Eyeball Mk 1 VMC terrain avoidance .. which, likewise, is only much use for the odd significant obstacle in an otherwise benign landscape.
The problem usually is (OEI) trying to match shallow climb gradient capability to one's perception of the terrain gradient ahead .. as a rule, it doesn't work too well at all.
So how to do it properly ? Someone has to do the work ahead of time in the traditional manner (either manually .. takes forever .. or using whatever fancy electonic aids might be available to save time on the number crunching).
Probable outcomes on the day if you don't have a well-engineered pre-planned escape protocol ? .. either you get away with it, go to the pub, get plastered, and sleep like a baby (depending on how big a fright you received ... or you, and your passengers die ... simple, really.
What saves the day overall is that
(a) most runways are reasonably benign and a half-intelligent pre-takeoff plan will see you right
(b) most failures are somewhat after V1 and, providing that you have kept your AEO climb profile well above the OEI animal .. you will have a measure of fat, the measure depending on how far out the failure occurs.
If (a) and (b) don't apply, then reality is that all the buzzwords and weasel words count for naught .. if you find yourself in a nasty terrain situation, OEI and post SID turn and the escape hasn't been figured out ahead of time and isn't right there on your pad in front of you .. then you are up that well-known creek without a paddle.