There is 2 types of agencies, most do use a CRM system but not everyone.
CRM focused agencies: These normally have strong policies and ways of working. everyone works in the same way, using set forms and emails. They also have a very black and white work method
Manual method: Some agencies (mainly smaller ones) might use a manual system, where they keep manual notes and not using a standard approach. You will normally find once a company grows, they need a CRM to prove for audit reasons and for great customer care, to have a set process.
HtE Recruitment uses a database called EBoss, which is really easy to use.