No, group membership is already established in /etc/passwd

Primary group membership is established in the /etc/passwd entry. Every user must be a member of at least one group, sometimes referred to as the default group. Membership in that group is specified by the GID in the /etc/passwd entry. So technically the user doesn't need to be added to that groups membership list in /etc/group. However, if the user is going to be a member of any additional groups he or she must be listed as a member in /etc/group.