"We have the ducks."
In the English sentence: "We have the ducks" the direct object of the sentence would indeed be "the ducks" and thus accusative. However, this is not how the grammar of this sentence translates in Turkish.
The English translation of "ördeklerler bizde" only includes the word "the" to indicate location, i.e. that the ducks are currently with us. This sentence does not indicate ownership. Without the word "the," the English translation would imply that we just own some ducks. Although you are right to recognize that the word "the" usually indicates a definite object and that definite, direct objects (as opposed to indefinite ones) take accusative case endings in Turkish, in this case the English translation includes "the" only because this is a locative sentence.
Lastly, the accusative case is only for direct objects of verbs, and the locative suffix attached to a pronoun - bizde - is not a verb.
- My original reply did not show up for some reason. Re-writing it again
"No, it's not correct, and here is why:
Suffix -i (after -imiz) indicates Accusative case, implying that some sort of action (transitive verb) will be taken on the object (Ducks). As there is no transitive verb in the sentence, Accusative case cannot be used.
Suffix -imiz indicates belonging to Us, plural of the third case (We). Nothing in the english version indicates that Ducks belong to Us. Article "the" completely changes the meaning of the sentence no longer making it possible to derive from the context that Ducks are Ours.
"Ördeklerimiz var" translates as "We have ducks" (like any specific ducks). But as I have indicated before the sentence is ambiguous, and I cannot imagine a situation where you would use this sentence in both of the languages."