Like
agreeing subjects, objects that agree with a noun class marker on the verb
exhibit adjunct characteristics. In the following, I will present a number of
supporting arguments from different sources.
With
pronominal noun class prefixes on the verb for subject and object, all word
order permutations are grammatical:

This seemingly nonconfigurational behavior is, of course, expected if
agreeing arguments are analysed as adjuncts. The Siswati facts in (23c,d) below
correspond to (22e,f) in Zulu and show that an agreeing object is free to adjoin
pre-verbally, which is ungrammatical for non-agreeing objects in (19 c,d).
(23)

(23a, b) show that an agreeing object may not intervene between the verb
and a manner adverb. Thwala 1996: 233 thus argues that such objects have the
same distribution as sentential adverbs, i.e. they are TP-adjuncts. This raises
the question of whether there is a subject-object asymmetry: after all, the
subject was shown to occur between non-agreeing objects and manner adverbs at
least in a contrastive reading. My data do not show whether a contrastive
reading may save a pre-adverbial object as well, so I will not further speculate
on potential differences here.
In
double object constructions, Siswati allows either THEME or GOAL agreement on
the verb. Similar to simple transitive constructions, the non-agreeing object is
required to remain adjacent to the verb, such that neither adverbials nor
argument-type adjuncts may intervene. (cf. Thwala 215-216). In terms of
agreement and adjunct-licensing, this behavior is just as expected.
Van der Spuy 1993 discusses
phonological evidence showing that agreeing objects are not located within VP
even if they occur post-verbally. In Zulu, phonological phrases are marked by
lengthening of the penultimate syllable in the phrase-final word. Van der Spuy
1993: 351 observes that verbal complexes with an object NC marker undergo
penultimate lengthening to the exclusion of overt object DPs. Assuming that
phonological phrasing reflects syntactic constituency[1],
he concludes that agreeing object DPs are not located within the XP containing
the verb.
[1] Proposals for syntactic structure determining phonological phrasing include Selkirk (1984, 1995), Nespor and Vogel (1986), Ghini (1993), Truckenbrodt (1995).