Despite Trump's education secretary pick, the United States is unlikely to move in the direction of a greater percentage of religious schools. It is likely that he will support measures to enable new private religious schools to be created, but religion will never be a factor in public school education in this country. Too many on both sides of the aisle are in favor of the separation between church and state for that to happen.
No, this will not cause a smaller number of non-religious schools, but it may make it harder for the families who don't have a religion or people who don't follow a certain religion to send their children to school. It just seems like Trump's pick for education secretary wants public schools to have daily prayer, which may be unconstitutional.
Trump pick for education secretary believes churches should be more involved in education: this is not leading us down a path towards fewer non-religious schools. It is purely more rhetoric to scare people into thinking as much. Given the state of government schools and the stupid students that are being churned out on a daily basis, perhaps God in said schools would be a great thing.
Even though this person might have her own personal opinions, there are still constitutional safeguards that make sure people get the education they choose. A person still has a right to a free and appropriate public education. There will be more options with freedom of choice, not less. This person will have new ideas, but can't fundamentally change everything.