My hunch is that there can be constituent tests for each language that work, but not each individual test would work for all languages.
Exactly. (Unless some languages don't have constituents. Perhaps unlikely.)
I really wish I knew an agglutinative language or one with a really different syntax to test this on!
I don't think it would necessarily be the large scale typological differences, but rather the small details such as exactly what sort of clefting (if any) a language allows, and this could vary even by idiolect. It's not a question of isolating vs. polysynthesis (or anything else on that scale) but just the details.
As for agglutination, I've just been studying Turkish and I studied Swahili for a while.
Let's see--
1. Replacement: as well as it works anywhere, I don't see why it doesn't work there.
2. Pro-form replacement: in both languages, pronouns are relatively uncommon but I think they're usually grammatical even for light "it" uses. However, objects in Swahili are prefixed to the verb sometimes, so replacement would end up with a different look, something like Spanish:
Veo la cosa = see.1S the thing = 'I see the thing'
La veo = it see.1S = 'I see it'
Beyond that, neither language has a very good translation of English "do", so I don't know that "do so" would work out very smoothly. There's "yapmak" ('to do') in Turkish which works for "what are you doing" but I don't know about the abstract sense of "He does too"-- in fact, I'd think not.
Note that in Turkish there is no use of "I do" in answer to a question. You'd say-- "Do you read [the book]?" "Yes, I read."
Beyond this, I'm not familiar with the full lexicon of the languages but I don't know of other words to test other categories.
In short, it would work fairly well for NPs (or DPs) but probably not much else.
3. Coordination
VERY limited in both languages, so it just wouldn't work out as a general test beyond categories that easily coordinate. You can use "na" in Swahili or "ve" in Turkish to coordinate sentences, but it's awkward and subsentential elements don't always work that way, with "na" meaning 'with' sometimes, and in Turkish juxtaposition taking the place of marked coordination often, even in NPs.
4. Ellipsis:
In Turkish this would perhaps work well-- almost anything can be elided, sort of like Japanese. But it's kind of messy when potentially multiple constituents can be missing at one time.
5. Movement:
Probably would work fairly well in both. The word order is fairly flexible in them, so it would be easy to apply.
But in other languages like Latin (or Dyirbal) subconstituents can be split, so that gets messy. There's an interesting puzzle in Swahili:
Ali wa-na-soma na JumaAli 3PL-PRES-study NA Juma
~~Ali study and Juma.
'Ali studies with Juma' or 'Ali and Juma study'
That seems like a problem for constituency to me.
An interesting example from Turkish is:
Ben iyi bir öğrenci.I good BIR student
'I am a good student.'
BIR is the numeral 'one' acting as an indefinite determiner. I can't really understand how far along this grammaticalization is, so I didn't gloss it specifically.
The phrase "iyi bir öğrenci" means "A good student". I have no idea what's going on with that syntax. Oddly enough, 'bir' can show up in what otherwise appear to be verbal compounds:
bir kitap okuyorumBIR book read.1SG.PROG
'I am reading a book.'
In a definite context, we would find kitabı, marked with accusative. The reason it isn't marked with accusative in the above example is because it is a verbal compound. Yet 'bir' appears there somehow. A mystery.
6. Book titles:
Sure, why not? I don't know of any reason why this would fail for these languages. Of course there may be certain limitations of what is required to support some other word, so maybe some things would have false negatives on this test.
In short, the tests apply differently, but probably (if adjusted properly) would work out just about as well in these languages as in English, but not without some adjustments.
There are some complicated details with morphological versus syntactic realization of elements though!