No, the reason she cares about that war is her love for John Smith.

In the beginning of the movie, Powhatan and his warriors returned after defeating the Massawomecks and Pocahontas did not seem care a little bit about that war. Meanwhile, she was "busy" thinking about her dream and standing on a cliff.

If there was no John Smith, Pocahontas will view the war between her people and the Englishmen as she view the war between her people and the Massawomecks. So she will not care to make peace.

I think she would still worry about her people fighting, the English had stronger weapons and they didn't know how to treat their wounds. However she wouldn't be as certain that talking to the settlers would help if she didn't meet any of them.

I think she would definitely care because despite the fact that she seemed to be more into her own dreams in the beginning of the movie, it doesn't mean she didn't care about her people. When she first met Smith she wasn't yet in love with him, but she tried to make him understand the importance of accepting different cultures and things he didn't understand before. I'm pretty sure she would have done anything to prevent her people getting hurt. In the second movie she thought Smith was dead and still cared about her people & traveled to the New World for them in order to talk to the King.

It would be like in real life...she cared not because of a Man, but because she was a kind, caring, and curious person. She did not need to know a englishman or be in love with one to be compassionate.