I think he did (cover it it well). There is evidence of course (his cuffs, the shardblade if anybody finds it) but it's all circumstantial. Nothing concrete places him at the scene of the crime. Unfortunately he had motive, and this will come off as an assassination by somebody, with heavy suspicion falling on the Kholins. It is sort of a locked room mystery (only someone in Urithiru could have killed him and they likely have an accounting of everyone there, though depending on the traffic and when the body is going to be discovered there could be some confusion in that issue.). Of course given how Alethi act about assasination even if it is proved it came from the Kholin camp no one will call them on it publicly. It will erode Dalinars position of honor though. Actually it will probably do that anyway based on suspicion alone.
And it isn't out of character. He has hated Sadeas since the beginning. He is a soldier, already used to killing. It's not like he is going to feel guilty about it. Maybe about the circumstances, but not the murder itself. He knifed a dude in a dark alley, but it isn't that different from swinging a Shardblade through a bunch of Parshendi. Hell, it's actually a lot fairer. Sadeas had a chance to fight back.