Yes. Because they never know who the assassin was.
Just changes a bit of dialog in certain points, but nothing else changes. I tried it!
I don't believe the Civil War quest line involves the Emperor himself in any way, so you should be safe.
It's bad for roleplaying purposes, though. But nothing changes, except dialogue a bit.
Yeah, my character was a Legion supporter who pledged herself to protecting the Emperor and Empire. I ended up having to head canon that she thought the Emperor was someone that just had to die.