The entry-level CAMP certificate might be more practical and cheaper than going for the PMP. I think the advantage of having the certificate is that it establishes a baseline for all managers in terms of knowledge or skills and allows everyone to communicate using a standard vocabulary regardless of the field you belong to. This is important because the quality of education varies from institution to institution. Jargon can also be highly idiosyncratic. You might be able to convince an employer that your experience plus the CAMP is enough plus it would give you an advantage over someone without any form of certification.
Given the level of responsibility associated with a job, a PMP certificate might be a waste of time even if a recruiter requests it. Recruiters are not good at evaluating skills so they ask for credentials. The NYT had a story last month about a law firm asking for bachelor’s degrees for entry-level administrative roles (which previously were filled by high school graduates) simply because they could. Why would you hire someone overqualified for a position? Do you think that person is not going to be bored and jump ship the first chance they get? Employers do very stupid things and then complain about employees not being loyal or that training is too expensive. Paradoxically, they then become more rigid and demanding when it comes to qualifications.
In the field of international development, many projects are managed by individuals that have no relevant training despite holding graduate degrees. An MA/MS is designed to prepare a candidate to pursue a doctorate therefore coursework in leadership, budgeting, human resources, strategic planning, organizational development and the like are not typically required. The knowledge and skills of a scholar differ from those of a practitioner. I decided to complete an MPA with a specialization in International Management for that reason. After trying to run projects as a Peace Corps volunteer, I discovered that there was a lot I didn’t know and had to make up as I went along. Experience is the best teacher but you don’t want to reinvent the wheel.