Absolutely. In fact, since in this AU Katte was never found out because that letter didn't get into the wrong hands, maybe once he hears Fritz is dead he does the one thing he can be sure Fritz would want him to do, get not just himself but also Fritz' beloved sister away from FW? During the first part of the trip (Berlin - Hannover) he and Wilhelmine are still numb and shellshocked, but once in Hannover when the adrenaline from the escape has gone and the reality of Fritz' death really has time to sink in, that's when they start talking (and shouting, and crying), especially since Wilhelmine otherwise has to play nice with the Hannover cousins (or their representatives, depending who is there). Once she hits upon her vengeance idea and heads towards Vienna, she asks him to come along again (a noble woman travelling alone still needs an escort, and whether she admits it out loud or not, he's the last thing she has of her brother - and vice versa, I guess).