The problem, always, will be that the escape flight path can be quite variable from one runway to another.
While there is a climb gradient penalty with turns, and this increases with bank angle (which is why the default maximum is 15 degrees to keep things under some sort of control) the turns are required, in general, to avoid the rocky bits out there. Keeping in mind that the rocky bits might be on the inside, the outside, or both sides of the turn, and that the required bank angle is tied to the turn radius and speed, both bank and speed are critical in tiger country departures for terrain clearance .. not to mention getting the start turn point correctly flown. Generally, the designer will include some flexibility to accommodate the realities of flying the departure and these parameters should be declared for pilot information. However, at the end of the day, an OEI escape in tiger country is an extremely critical and demanding flight manoeuvre.
If the automatics are up to flying to the required accuracy, there is no philosophical reason why an escape can't be programmed into the database. Indeed, if that is feasible, it provides for a better solution than getting the human pilot to fly the escape. One of the problems will relate to whether the particular system will permit pilot programming to the required accuracy or not.