"the activity, set of institutions, and processes for creating, communicating,delivering, and exchanging offerings that have value for customers, clients, partners, and society at large." [1]
Having worked with the people who run such campaigns they would absolutely describe themselves as marketing practitioners, many move between public and private sector during the course of their career and the skillset and techniques for doing both are completely fungible. Worth remembering also that public health campaigns are paid for with public money.
Yes. An agenda.
Personally, and I have held this opinion for more than 2 decades now, is that I don't see any practical difference between marketing campaigns and political propaganda. They are both trying to influence an audience for their own benefit, and are constantly trying to sell something.
Services. Check. Products. Check. Ideas. Check. A way of life. Check.
An agenda? Check.
(EDIT: make quoted text appear in italics)
For example, I wouldn't say this was political, they have nothing to sell: https://www.youtube.com/watch?v=QO5pI5pmYE4 (railway safety)
The campaign that started the "5 a day" thing was called Change 4 Life, and seems closer to education and information than propaganda: https://www.youtube.com/watch?v=Nb0fLYdPEPM
https://en.wikipedia.org/wiki/Change4Life
http://www.nhs.uk/Change4Life/supporter-resources/downloads/...
This was a public health awareness campaign, and given the huge number of TV (and other) adverts they had, I'm surprised if people didn't see it as such.
I wouldn't call the road or railway safety campaigns 'marketing', but they're also well-run campaigns with lots of visibility and sometimes memorable phrases.