Is Jesus really 'a god' in John 1:1 (New World Translation)?

No - "a god" is a mistranslation, though it starts from a real feature of the Greek. In John 1:1's third clause the word for "God" (theos) lacks the definite article that the second clause - "the Word was with God" - has, and Jehovah's Witnesses argue the article-less theos should read "a god," preserving the distinction between the Father and the Word. The missing article is doing real work - John has just said the Word was "with" God and is not about to collapse the Word into the Father (the ancient error of modalism, which orthodoxy also rejects) - but it does not license "a god."

The problem is the leap from "no article" to "therefore 'a god.'" That inference does not hold in Greek. Philip Harner's 1973 study showed that anarthrous predicate nouns placed before the verb - exactly the construction here - are usually qualitative: they describe the nature of the subject rather than counting it. The clause means the Word had the very nature of God. Daniel Wallace's standard grammar reaches the same verdict: theos here is neither definite nor indefinite but qualitative - the Word fully shares the divine nature while remaining personally distinct from the Father.

The elegance is in the balance. Had John put the article on theos, he would have made the Word identical to the Father - modalism. Had he meant "a god," he would have made the Word a lesser divine being alongside God - polytheism, from an author steeped in Jewish monotheism. What he actually wrote threads the needle: the Word is fully God in nature, yet not the person of the Father. "A god" is the one reading the Greek and the context will not bear.