I think some would. The reason many won't is because they believe him when he would say it wasn't true. He'd say, "believe me" and they would. I mean, if we go farther towards the charismatics, who are like what the evangelicals used to call crazy (but are now becoming like), those people believe people can speak in tongues when they are just saying gibberish. You're talking about people that *want to believe*.
My mother, while her views have evolved over the course of my life, is heavily influenced by evangelism. My father has forbid her to go to the Baptist Church -- and she listens ("wives, obey thine husbands'), and so she's been tempered back towards reality... But she despises Trump because she finds him morally disgusting. I think her faith largely commands the reason she feels this way.