Is arithmetic coding restricted to powers of $2$ in denominator equivalent to Huffman coding?

With restriction to $$\frac{k}{2^n}$$ as line segment ends, does arithmetic coding degrade to Huffman coding? As far as I can tell, each symbol will be encoded with an integer amount of bits, which is the same as Huffman coding. However, I'm not sure how to prove that arithmetic coding with this restriction is optimal for integer code lengths.

Arithmetic coding "degrades" to Huffman coding if all of the probabilities are of the form $$2^{-k}$$. Or, to put it another way, when the Kraft-McMillan inequality is an equality.