Yes, they should use quotes by Jerry in their teaching. He was a very smart man, and his works should be known by everyone who practices the religion his quotes pertain to. He knew a lot about what to say to make people believe in a religion and want to follow it.
Sunday school teachers can use whatever quote they want in their teachings. They can practice whatever religion, teaching they want, and should therefore use any quotes of Jerry Falwell as they wish, as long as their members and people of that church agree upon it. Sunday school is not part of the public school system, and therefore have the right to use whatever they wish in their teachings.
As long as the Minister of Education at the church is pleased with what a Sunday School teacher uses in her class, she should be allowed to use that material. It is a volunteer position. If the church is unhappy with what she is teaching in her class, they will inform her. She can, at that point, eliminate that from the curriculum or find another church.
In spite of the mega church movement Jerry Falwell created, he turned out to be extremely intolerant and racist. He reportedly was anti-gay, anti-blacks and against labor unions. As time went on he seemed to be become more intolerant and more open in stating it. His beliefs are not something we would want to quote in today's world.
Jerry Falwell spews some of the most ridiculous, bigoted garbage I've ever heard out of a human being's mouth. His words are grating to the mind of an adult, which is bad enough, but they would have an extremely caustic effect on the mind of a child. Children should be nurtured and protected, not poisoned.