A copula, by any definition of "function word" vs. "content words" that I've seen, would be considered a function word.
But the verb "to be" may not always be a function word. Consider the famous phrase, "I think, therefore I am". It contains two function words, "think" and "am". The verb "to be" is considered an auxiliary verb in most cases, but in this case it's a non-copular, existential form of the verb. So "am" is a content word as it is not linking or connecting anything but is here used as a synonym for "exist".
In a less famous example, the sentence, "I think, therefore I am thoughtful", it becomes merely a function word for the word "thoughtful".