I think most of us have been around someone who only does good things if other people can see that they are. I also think a lot of us baulk at the idea. It just seems wrong.
However, Machiavelli brings it up in The Prince. Whether or not The Prince was satire, the best satire does have snippets of truth of some sort or another in there. Motivationally, Machiavelli may have wanted the Medici's to be less openly contemptuous of common morals. Whatever his motivations, Machiavelli was not a moron.
I think the line "good must be done and be seen to be done" is important for organisations, at least. This is an important demarcation that a lot of people ignore, in that behaviour that an organisation engages in is not necessarily good for an individual (and visa-versa). People tend to care about their family, friends, and their immediate surroundings. Many organisations are created with a goal in mind, and don't need to eat, sleep, or pay rent.
People should not denigrate people or organisations doing what's necessary for survival. Ethically, we recognise that self-preservation is an important instinct. While we consider those who go against in heroes, we do not denigrate (mostly) those who would place their own immediate survival above others. Similarly, we should not denigrate organisations for taking actions that ensure their survival.
Recruitment and retention are for organisations as eating and breathing (and pooping, I guess) are for us singular organisms. People are literally organisation food, consumed and re-purposed to whatever tasks are deemed necessary. It's a kind of weird analogy, but makes sense if you think about it a little.
Doing highly visible "good" is important for both recruitment and retention. Internally, they provide energy and vigour. Externally, they make the organisation look good, even to those who do not even consider joining.
What "good" is in this sense is a little bit nebulous.
Many organisations have a moral imperative guiding them. The American Civil Liberties Union has ethical guidelines that are, in part, the definition of the organisation itself. Of course, not all organisations have moral goals. That is, they don't mention morality as part of their goals. Presumably there are a couple of immoral organisations out there.
The societies they operate in also have their own moral codes. This gives its own limiting factor to an organisation. An act that an organisation considers "good", if not aligned with a society's "good", has a very high risk of alienating the organisation from the general population. The Westboro Baptist Church (assume its goals are sincere for the time being) is an example of this. They might think there is some moral duty in protesting homosexual soldiers' funerals. While they might think of this as "good", they have failed to consider the society they live in.
Of course, they might have, but for an organisation to prosper it must be aware of the society it is attempting to operate in. It's all well and good (aha) to have moral ideals of how society should work, but societal changes are typically slow, and ultimately an organisation (if it believes in its moral ideals) should want to enact the change as painlessly and quickly as possible. That change typically only comes with a decent amount of the population involved.
Even for organisations that do not have a moral imperative, say a local board gaming club, it is important that good works should be done and seen to be done. Without an internal morality to clash with society's, they should have more freedom to do so. Charity, joint projects, doing things with the local amputee orphanage, that sort of thing. But it IS tremendously important that such things are advertised. Not that without that they are pointless, but rather that the effect is far more healthy for the longevity and activity of the organisation.