It depends on exactly how you characterize "white," since at the time "whiteness" did not exist in the way that we understand it today; but the short answer is yes, men born to European parents - either on both side or only on one - did have influence and fame among Native American groups, and took leadership positions during wars and other conflicts.

One of the more famous is John Norton, otherwise named Teyoninhokarawen, who rose to prominence among the Mohawk and other Six Nations peoples. He was born in Scotland to a Scottish mother and Mohawk father, joined the British army, and eventually deserted, and was adopted into a Mohawk family under another famous chief, Thayendanegea or Joseph Brant. He acted as an interpreter and warrior, and led war parties during various conflicts, including the War of 1812.

Charles Michel de Langlade, an Odawa war leader, was another. His mother was Odawa and his father was a French fur trader. He is represented historically both as a Frenchman - he was briefly the commandant of Fort Michilimackinac, in Michigan (where he was born) around the end of the French and Indian War - and as an Odawa. He was metis, or of mixed-race heritage which is today recognized as a distinct culture, but at the time he identified (and was identified) as either French or Odawa, as need arose.

This was not altogether uncommon, especially in middle ground regions like the Great Lakes, and was a result of cultural practices among Native groups and white settlers. On the Native side, ritual adoption was a widespread practice that brought captured white children into kinship groups to be raised as full members of the group - Apekonit, or William Wells, an American boy, was raised among the Miami, considered a full member of that tribe, and was eventually brought into the United States Army and served as an Indian agent in Chicago until his death early in the War of 1812, for instance - that was, in part, meant to replace young warriors who had been killed in previous conflicts. White settlers, too, used capture and kidnapping - usually taking survivors of raids or burned villages - and raised young Native boys as members of the family. John Norton's father, for instance, was a Cherokee who captured and brought back to England to be raised.

Intermarriage was extremely common among French fur traders, but it should be understood that a sort of cultural fluidity was the norm among many of the Eastern Woodland groups of Natives. Men would sometimes take their wife's nationhood or identify themselves as members of the tribe they married into, and they might consider themselves British, American, or French, and wear clothing, build houses, and live with certain habits that were meant to exemplify kinship and loyalty to that group. Chiefs like Little Turtle and Blue Jacket (Miami and Shawnee, respectively) wore European style clothing and lived in European style houses, and even raised cattle on their own ranches, and both of these men had been participants and leaders in St. Clair's Defeat, the worst proportional defeat of the United States Army in history just a decade or so before.

So, to make a long story short, yes, there were what we might consider white native chiefs.