I don't think there actually is such a thing as obstacle cover in D:VG. Obstacles can be used (there are rules pertaining to them such as climbing), and I believe that, if used, they do affect movement and may block LOS. Given this...
Can, as in some systems, a trooper gain full cover bonus but ignore the corresponding penalty if he is in contact with the wall firing at an enemy in the open on the other side?
This is strictly speaking not possible under the rules. You could designate the wall as terrain cover, but it would not lead to this type of resolution. The model benefiting from cover bonuses could be at either side of the wall from the attacker, for example, provided it is close enough (touching if PI, within 1" if SI) to it, and contrariwise would suffer cover penalties if firing accross the wall even if touching it.
I assume a trooper is considerd out of LOS if he can't be seen behind a wall, WYSIWYG style, or is that abstracted (not necessarily a bad thing)?
It can either be abstraced by designating the entire area as area cover, or you can designate the wall an obstacle. I think the implication is that only fairly tall obstacles, such as high walls, should actually be designated obstacles, while low (say below 2" height) stuff would simply be indication of area cover. So the LOS problem in combination with obstacles should actually be negligible for most models.
The path of least resistance would be to place the low walls and rubble piles so that they mark the boundaries of an area cover and make any obstacle walls so high that there is no particular problem at identifying them.