Really, the only difference in the two timelines was Tasha Yar vs Worf in terms of the command structure of NCC-1701-D. Why would there not have been additional timeline changes in terms of command structure / staff on NCC-1701D after the timeline divergence in "Yesterday's Enterprise"?
Surely, if Picard had even still been given command of the Enterprise (Encounter at Farpoint) in this timeline he would have chosen a completely different crew in this timeline than the other timeline for "war time purposes". I can see Data or Tasha being good choices, but why Geordi, Wesley, or Beverly if Picard was thinking about "war focused objectives" in this timeline? He cared personally for Beverly and Wesley...
Finally, why would Guinan have not known something was "wrong" when she boarded the ship (initially) where the timeline would have surely been different (and she was boarding a ship "made for war" rather than "for peace")?