It really depends on the policy. Some policies only refuse treatment for "major" pre-existing conditions (heart issues, cancer, etc.), but will cover depression, anxiety, blood pressure, etc. Your best bet is to call the insurance company and ask them some general questions. I'd broaden your questioning so as to not raise any flags in case they say they will deny treatment. You could also phrase it as if you think your daughter may have an issue but don't want to run into insurance issues, so if it's going to count as pre-existing you will wait 3 weeks to get her into the doctor. Or you could tell them you just have some questions to determine if you want to take the coverage when you're eligible.
My mom used to handle insurance for Eli Lilly, and that's the advice she gave me in a similar situation a few years ago.