Can the president of a 501(c)(3) step down from the board in order to receive a salary from the organization?
Yes. But it may not be necessary.
There is nothing illegal about paying officers and/or directors reasonable compensation for their service on the board, although a great majority of public charity directors are volunteers and the Standards for Excellence promulgated by Maryland Nonprofits and being replicated by many state associations throughout the country call for directors to serve without compensation.
Even where directors are not paid for services as such, however, they may be paid for other services, such as service as an officer or as a consultant, lawyer or advertising agent. It is not unusual for a paid CEO to serve on the board of a nonprofit organization, particularly larger ones like universities, hospitals, private foundations, or trade associations. You may not want to have the paid president on the board of your organization, but it is not illegal.