How effective was the Dawes Act in promoting assimilation of Native Americans into white cultures?

Not effective at all.

There were many problems with the Dawes Act (1887). Land that was given to individuals tended to be inhospitable and not conducive to farming. (remember it was reservation land -- land the whites didn't want). Farming was such a foreign way of life to some tribes that they would not do it. Others who wanted to farm could not afford the seeds or equipment to make a go of it.
Furthermore, there were issues with how the land would be passed on to decendants. Children inherited the lands who had already been sent off to boarding schools.

Dawes felt that if the Indians had their own land, dressed in white clothing, and adopted white customs, they would become white. What he never took into consideration was that the Indian's spirit would always be Indian, and that would never change.