Polysynthetic languages typically show two defining properties: the systematic morphological marking of arguments through verbal morphology and highly flexible clausal word order. In an influential generative account of this generalization, the second property emerges as a consequence of the first (Jelinek 1984, Baker 1996): non-pronominal NPs are structurally represented in dislocated and/or adjoined positions, as licensed by each expressed argument (i.e. polypersonal agreement), via inflectional affixes or noun incorporation. A separate question arises about how "rich" such a system of agreement needs to be in order for flexible clausal word order to arise. We examine the interaction of overt agreement and word order in Cherokee (S. Iroquoian), whose system of verbal morphology does not have productive noun incorporation and shows restricted overt agreement with third-person arguments. The language nonetheless shows abstract polypersonal agreement; agreement morphology generally depends on relative properties of multiple arguments in the clause. Using a quantitative analysis of an annotated corpus, we find that whether an NP is overtly coindexed by a pronominal prefix has no effects on its placement in the clause, as consistent with a model in which verbs agree with all arguments in the syntactic representation. This supports the general criteria for morphological visibility in polysynthetic languages posited by Baker (1996, 2006), and suggests that the amount of non-overt agreement tolerated in polysynthetic languages is higher than previously assumed.