Yes, but this sort of structure is often intended to be surprising, and thus clever, witty, or humorous. We supply the missing words: "He is a manager and [he is] stupid." This is grammatically correct. However, we sense the grammatical difference between the noun "manager" and the adjective "stupid." It draws attention and surprises us. Here is an example of this structure. This is not humorous. It is from the work of A. E. Housman, a famous English poet: "I, a stranger and afraid In a world I never made."

You can say it, but it is not typical. When you join two entities with the conjunction "and", they usually have the same form: "noun and noun", "verb and verb", "adjective and adjective", or "complete sentence and complete sentence". To follow this convention, you would say "He is a manager and a stupid one."

He is a stupid manager.