"He is my guest."
Translation:Li estas mia gasto.
No, the accusative is not used after a stative verb. The accusative marks a direct object, which requires a verb of action. "He threw the ball". What was thrown? What received the action? The ball.
A stative verb reflects the state of the subject, so rather than a direct object it takes a predicate complement, which in most languages is in nominative case (Polish for example uses the instrumental case).
If the accusative were needed, however, then it would have to be "...mian gaston", because the whole noun phrase (in Esperanto, excluding the definite article) needs to be in the accusative, not just the noun itself.