Yes, earning a CPA makes you an accounting professional once you begin working as an accountant. You can earn a CPA and never spend one day in accounting, but do something else instead.
CPAs do not manage investments. They manage cashflow, accounts receivable and accounts payable, ie, see that the bills get paid and see that the client is not being cheated. They prepare tax returns, they can audit an individual's financial activity, or a company's books. You can do these things for a wealthy individual, but it will most likely be done as an accountant with a known company, not on your own, not until you are well-established in the profession.
A CPA CAN manage someone's investments, but they aren't doing so AS a CPA. They are doing it with additional accreditation as a Certified Financial Planner or other credentials of an investment professional.