Saying that a verb is copular, or a linking verb, is the same thing as saying that the verb has a subject complement. Certainly a verb can be transitive in one use, copular in another. It can't be both transitive and copular in the same use.

Is a linking verb an intransitive verb?

Linking verbs—those that join a sentence subject to its complement—are likewise intransitive. Common linking verbs are become, seem, appear, feel, look, taste, smell, sound, and be. Subject complements for linking verbs will be adjectives, nouns, pronouns, possessive pronouns, or adverbs of time or place.

Can a linking verb have a direct object?

A linking verb cannot have a direct object. Action verbs are the only verbs with direct objects.