Dividing data between test, learn and predict
Supervised Learning:

Do you have a saved time history of the data?  For a supervised learning set you need some churned="No" cases and some churned="Yes" cases, but it sounds like you only have churned="Yes" and the unknown cases e.g. current customers who may or may not churn.  With some time history you can go back in time and definitively label the current customers as churn="No".

Then it is very easy to split up the data.  And no, you probably don't want to predict on any data that you trained on since you can only train on it if you already know the solution so it will be a waste of time and throw off any metrics you might use to assess accuracy (precision/recall/F1) in the future.

Unsupervised Learning:

If you don't have saved time history of the data then this is an unsupervised learning set for which you have churned="yes" and churned="maybe".  You could then employ anomaly or outlier detection on this set. 

novelty detection:
    The training data is not polluted by outliers, and we are interested in detecting anomalies in new observations.

outlier detection:
    The training data contains outliers, and we need to fit the central mode of the training data, ignoring the deviant observations.

You can do either one but novelty is more powerful.  This is kind of a flip around as the novelty here is Churned="No" since all of your data is the confirmed Churn="Yes" cases.

Hope this helps!