Well I tried shockwaving it, but all it did was continue to tick and then blow up in my face. Once a grenade has finished its trajectory, it appears that it becomes a static object. ( I tried throwing a lift grenade and loosed a shock wave while it was bouncing.. nothing happened. )
In regards to your problem, the game normally provides covers that are close to each other- a simple roll to your left or right should solve your cover issues? I do have a sort of invulnerability when I roll, or at least I've never had my shields or health bar drop when I rolled.
Haven't tried timing a roll to dodge the aoe explosion of a nade though....
I've also found that if you kill an enemy before he throws the damn nade ( whilst he's in the throwing position ) he drops the nade. His comrades don't die from it though.