No, accusative is used for the definite direct objects of active, transitive verbs.
So "Duo başkan(dır)" is "Duo's the president."
But "Başkan Duo'yu seviyor" is "The president loves Duo." Duo is the accusative, definite, direct object of the president's loving.
And "Duo başkanı istemiyor" is "Duo doesn't want the president." The president is the accusative, definite direct object of Duo's unwanting.
Not exactly definite. And not strictly necessary, though you'll see it on Duo. It's honestly a really odd complicated use ending.
But! Let me slip you a secret link with the honest truth about this suffix, I think it's the BEST explanation I've seen (added bonus of it being short):
'To be' never seems to trigger the accusative in languages that decline by case. I guess it's because you could switch the nouns/pronouns and still mean the same thing (e.g. "Duo is the president" and "The president is Duo"), whereas the relation between a subject and object is asymmetrical ('Duo eats a sandwich' is not equivalent to 'A sandwich eats Duo.')