If there is a dominate peaceful faith, then other faiths will loose their role. Christ wouldn't be Christ. Muhammad wouldnt be Muhammad and so forth. We'd literally have to divorce our beliefs to conform with the foundation of the dominate religion. (Given the word why it's dominate).
Can dominate religions provide peace?
It depends on what your definition of dominant religion is. If by this, you mean a Religion which forces its beliefs on others, or pressures others to also believe, in what they believed, or discriminates against those who have a different religious believe, then, in my opinion it won't be able to establish peace, and most likely, there would appear conflicts and divisions between the followers of its own.
The Bahai Faith cannot be like that, as can be seen from its scriptures, it forbids Bahais from forcing their belief on others or even defend their own religion by use of weapons. Also, the Bahais, believe Jesus, Muhammad, Buddha, Krishna...were all the Truth, and Islam, hinduism, buddhism, zoroastrism,...all had the same and one divine origin, so they do not change their mind, about truth of the older Manifestations. Off course, the Bahai Scriptures provides a new interpretations of some of the sayings of the Previous Manifestations, because it says, some of Their sayings were not to be taken literally, and must be interpreted Symbolically or Mystically. But what is wrong with this, or what harm is in this?