Yes and no.

Obviously all Commonwealth realms have the same head of state, that's what makes them a Commonwealth realm (which is different to a member of the Commonwealth of Nations). So they are in personal union.

But there are those who argue that it's more than personal union. There are huge cultural and historical ties, as well as the fact that there are some vestigial constitutional quirks that tie the countries together. Some of the countries still use the Privy Council of the United Kingdom (usually on as a gesture of good faith) even though through the process of becoming a dominion they can establish their own.

Put simply though, it is a yes. At best it's a yes with conditions.