No. The normal path is Shopify billing: the customer pays the first order with a card in your usual checkout, Shopify stores a subscription contract and charges the renewals. No Mollie account is involved, and nothing in the app asks for one.
You need Mollie for one thing only: letting customers start a subscription with iDEAL, Wero or Bancontact. Shopify cannot save those methods for a later charge, so we run them ourselves. The first payment through your own Mollie account creates a SEPA Direct Debit mandate and the app charges every renewal against it. That is worth doing if you sell in the Netherlands or Belgium, where those methods are how most people pay, and it is dead weight otherwise. "Accept iDEAL and Bancontact: connect Mollie" is the setup, and "How Mollie subscriptions renew with SEPA Direct Debit" is what happens after.
Stuck on any of this? Open the chat in the bottom right corner of the app and we will help you set it up.