Does a new customer belong to a customer account?

No, creating a customer person or organization only establishes this party as having some kind of selling relationship with you.

You need to create at least one customer account and one customer account site with a bill-to purpose for the customer record in order to properly record and account for both sales transactions with the party and other attributes of the selling relationship with the party.

When you create a customer manually, the customer account is assigned the profile DEFAULT. When you import customers, there is no default profile assigned to the customer account. You must designate a customer account profile in the RA_CUSTOMER_PROFILES_INT_ALL table by specifying information for the CUST_ORIG_SYSTEM and CUST_ORIG_SYSTEM_REFERENCE attributes, and leaving blank the CUST_SITE_ORIG_SYSTEM and CUST_SITE_ORIG_SYS_REF attributes.