I don't think Picard would have surrendered or anything like that. But, he is a peacetime captain, not a wartime captain, and he would have been willing to make more concessions in order to prevent a war, and the Dominion would have taken advantage of that.
But then again, if Sisko were commanding the Enterprise they would have gone to war with the Romulans in The Enemy or The Defector.
Odds are, he actually wouldn't. Many of Sisko's actions were dictated either by his role as the Emissary or by the war with the Dominion. Had he been in command of the Enterprise
with his wife and son instead of the XO of the Saratoga
, he likely would have been as much an advocate of peaceful resolutions as Picard was.
And Picard might have been able to calm down the Klingons in Way of the Warrior.
Unlikely. The Klingons were the outright aggressors in that story and were out for blood regardless of who was in command. The Klingons withdrew from the Khitomer Accords after the Federation condemned their invasion of Cardassian space and DS9 became a target when it offered asylum to the surviving members of the Cardassian government. Unless Picard was willing to hand them over to the Klingons for execution, the attack on DS9 would have happened regardless.