Did Sun Tzu believe in peaceful negotiations more than battle?

This is an interesting question, and a valuable one worth asking. Ultimately, I would say that Sun Tzu recognized that warfare entails a kind of gamble. Indeed, he does write about the strain a war can put on a country's economy and the spirits of its people, as well as the devastating effects which follow defeat. That being said, there is a pragmatic and calculating streak in his understanding of warfare: for Sun Tzu, the ultimate end is victory, and his treatment of diplomacy has to be viewed in light of that.
For Sun Tzu, warfare tends to be driven largely by questions of judgment and military intelligence. The stakes of armed conflict are such that caution becomes a rule: for Sun Tzu, one should not enter into battle unless the military and strategic calculus ensures victory, and even then, I believe he recognizes that said battle might well entail additional costs. From that perspective, I think Sun Tzu would prefer peaceful negotiations to pitched battle, assuming that both options lead to the same ends: the advancement of the interests and political dominance of one's own country. From that perspective, if the choice is between combat, and accepting the peaceful surrender of an outnumbered and demoralized opponent, Sun Tzu would in all likelihood prefer the latter. However, the key here is that these peaceful negotiations ultimately need to serve the interests one's own side. For Sun Tzu, a general seeks to accrue the various military and strategic advantages, while denying them to the enemy, to the ultimate purpose of defeating the enemy. That is the goal, and it is in the context of that goal that both peaceful negotiations and battle ultimately have to be viewed.