Board Thread:Questions and Answers/@comment-5693502-20140410203934/@comment-5398287-20140412200014

I don't believe so, since Kidou seems to be exclusive to Souls (proof coming from the fact that Kuukaku Shiba, who isn't a Shinigami, can use Kidou). Meanwhile, an Arrancar is still a Hollow, but with a Shinigami Zanpakutou - so they couldn't use Kidou.