That out of the way, faith is the belief of something without evidence.
I'd agree with that.
Therefore you could not move from a faith based belief and be wooed to a different belief through evidence and still retain the faith. You can make the logical conclusion from the evidence presented to you and decide which one you want to go with. That would be based on critical thinking, as you are analyzing the premises and evidence, and thus removing faith from the equation.
That doesn't imply this though. Why can't I consider faith and evidence at the same time? I could then decide to favor either of them in determining my final belief.
Your conclusion might work if we defined faith as belief contrary to evidence. As in, contradicts evidence.
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