I would say yes because I support at least one organization that's been using for such purposes for nearly 7 years and several others for 3 - 5 years. This is one of the core features of CiviCRM and it's been getting better at it over the years. Whoever is in charge of this endeavour will need to learn how the contributions system within CiviCRM works and how it relates to Memberships, Events, etc and how to run reports but it is definitely all there.
EDIT: This is the Financial Accounts area of a recent build (there is a substantial learning curve).