No. There are various distinctions, such as how they interact with the verb, how the semantic structure is generated, whether there may (or may not) be some additional null elements (empty nodes) between the V and complement, how the verb selects the complement, etc. And then there's something about case assignment-- in that sense in particular it's very much not an object, because an object is assigned accusative case.
But in terms of the BASIC tree structure (constituency), yes, it looks the same, when you omit labels and don't add any extra intermediate categories.
[Subj [V Obj/P.Adj.] ]
But there's a lot more going on than that.
To consider a different example, in Arabic the verb "to be" is not used in the present tense under normal situations. But when it is used (for example, in the past tense) you get accusative, not nominative. So maybe it's not really a copula but actually a transitive verb.