But the application form isn't asking for credit card info. (Does anyone know whether they ask for that later in the approval process?)

In any case, the fine print says that participants have to purchase after the expiration of the free period in order to to continue. Nothing is mentioned about having to give payment info upfront, such that the account automatically transitions to payment.

Participants who are already paying customers will have their payments suspended for that period, so I think for them it will automatically lapse back to paid, at least if their payment method is up-to-date.