Does 'throwback' require an indefinite article?
Solution 1:
In the example you have given, an article is required. "He's a cheeky little throwback." Throwback is a noun, and so an article is required. The article would usually be the indefinite article, although in some cases, such as to emphasize uniqueness, the definite article could be used, such as "Isn't he the cheeky little throwback." Although, it would normally be the indefinite article.