[H]ow could we ever test this? We can't test it because there's no way to redo a particular interaction between two organizations using different individual components.Sure, but there's a whole lot in social science that we can't test. Only logical empiricists would argue that only things that are empirically testable can be legitimately considered as knowledge. And logical empiricism is pretty much dead because it doesn't even satisfy its own conditions. That doesn't mean, of course, that we should go the other way and renounce empirical analysis - we need more of that not less - but rather that we can't expect everything we need to know to present itself conveniently for our 'testing.' (We need to be more radical in our empiricism!)
This is the problem with talking about 'mechanisms,' which I must admit always makes me feel a bit queasy. It's difficult to use this language without implicitly (even unintentionally) endorsing the 'mechanistic universe' image that is so wrong in so many ways and so thoroughly opposed to all we hold dear in these corners of the blogosphere.
But I take your point - we mustn't just take the standard categories of social science at face value. Ideas such as culture and civilization have long and ignoble histories. They are slovenly, rotund, catch-all categories that should be avoided.
But that doesn't mean, however, that we can't talk of social aggregates that possess the capacity for constrainment, enablement and downward causation. It just means that categories that encompass millions upon millions of people who have less in common than they do in difference should be avoided because they tell us nothing about those people other than that some people like to group them all together for no good reason.
Such a thing a 'Muslim culture' or 'Islamic civilization' surely doesn't exist except for its manifestation in various public discourses (and although this mode of existence gives them a certain degree of reality it takes an enormous amount of effort to territorialise these discursive assemblages, which I think is really rather the point - they're like an empty sack, they don't stand up if you're not holding them there!).
In the example you raise I think we would do well to recall DeLanda's useful notion 'redundant causation' - that is, we can talk of wholes insofar as we would gain nothing more in the subject of our analysis if we considered the parts as well. Certainly there are many instances where this is true. If we weren't able to 'frame' our world in this way we wouldn't be able to do or think anything much at all.
So, we shouldn't talk about the enculturating effects of 'Muslim civilisation' but we may be perfectly justified in talking about the enculturating effects of particular sects, particular mosques, particular geographical areas. We don't necessarily have to follow each individual person around indefinitely to grasp the requisite 'mechanisms' at play. Every analysis is an instance of abstraction - the question is whether this abstraction comes from real terms and whether it is abstracting properly.
But it is true, emergence is a very hard thing to pin down. It is not something that can be solved completely. This whole debate over emergence and mereology, we would do well to remember, largely replaces the agent-structure problem as it is in conventional social theory. It improves upon that problem in a variety of ways but it shares certain problems - there is a fundamental indeterminacy in both not just in fact but in principle too. With an indefinite number of causes acting upon an agent over an indefinite amount of time and with no possibility of isolating certain variables in a laboratory environment, we can't imagine causation in these circumstances following anything at all linear or determinate. We certainly can't do much 'testing,' it is true.
It'd be better to think of culture in terms of its other meaning: a culture of germs in a petri dish, say. Concrete objects involved in a complex, co-dependent and co-emergent mixture. It is down to the analyst to establish precisely the character of the mixture and perhaps it needs to be broken down into smaller, purer sections before it can be understood. 'Redundant causality' can help us make this connection but we can't ever hope for 'mechanisms' in any deterministic sense.
And remember: 'any sufficiently advanced technology is indistinguishable from magic.' We might not have gotten a handle on social emergence yet but that doesn't mean it isn't a real phenomenon any more than my not understanding how a car engine works means I can't drive it around.