No, because his authority as King of the UK is completely different from the position of Head of the Commonwealth. It doesn’t give him any additional constitutional authority, unlike the Chairman of the Board of a corporation would have.
And also, Her Majesty cannot make him the Head of the Commonwealth. Only the governments of the member-states of the Commonwealth can choose the Head of the Commonwealth.
“Empire” at that time has a meaning similar to the modern concept of a “sovereign state”. That is, the head of an empire did not owe any feudal allegiance to any other sovereign. That’s what the declaration that “England is, and has been, an empire” meant.
Missed the edit window: the phrase is actually: “this realm of England is an Empire, and so hath been accepted in the world,” from the preamble to the Statute in Restraint of Appeals, 1533.
I hope I’m helpful, but I’m not a Brit. 
The Balfour Declaration of 1926, the key statement in the Proceedings of the Imperial Conference of 1926, is usually seen as the formal recognition (note: not establishment) of the modern Commonwealth:
The Declaration stated that Britain and the Dominions (at that time six in number) were each:
The change in the 1949 declaration was that a country could be a republic and yet a member of the Commonwealth, without owing any allegiance to the Crown.
Only two of em.
There were four King-Emperors: Edward VII, George V, Edward VIII, and George VI.
So what is the significance of this new assignment? Does the head of the Commonwealth do anything other than gavel meetings to order, give a speech, and automatically give their consent to whatever the Commonwealth decides?
Does Mozambique get a say? They’re in the Commonwealth, but Elizabeth is not their Queen.
A majority of the Commonwealth countries do not have Elizabeth has their head of state. Most of those are republics (India, Bangladesh, etc) and a few have their own monarchs (Malaysia is one.)
The Head of the Commonwealth does nothing at all. The Commonwealth already has a Secretary General (currently Lady Patricia Scotland) who is the nearest thing it has to a chief executive, and a Chair-in-Office (currently Teresa May) whose job is hosting the Commonwealth Heads of Government Meeting, which happens every two years.
The sole function (if you can call it a function) of the Head is to be a “symbol of their free association” for the member countries of the Commonwealth. Since a symbol doesn’t have to be animate, never mind human - a flag, for instance, could symbolise the free association of Commonwealth members - this isn’t really a role or an office, just a title.
As others have pointed out, the title was created when it was decided that the Commonealth was to include a country which didn’t have the British monarch as head of State - specifically, India, which became a republic in 1950. Up to this point being a monarchy under the British monarch was seen as a defining condition of membership. If the monarch wasn’t going to have a role in each Commonwealth country, then it was decided that he or she was to have a role in relations between the Commonwealth countries, even if only a purely symbolic role. Hence “Head of the Commonwealth”.
I’m faintly amused by recent discussion over whether the next Head should again be the new British monarch. The Commonwealth doesn’t need a Head; it can function perfectly will with a Chair-in-Office and a Secretary-General, and the only reason for having one is to give the British monarch a symbolic significance that he or she wouldn’t otherwise have. If the Head is not the British monarch, there is literally no point at all in having a Head. So the question is not “Should the next Head be Wales, or someone else?”; it’s “Should we bother to replace the present Head when The Time Comes?”.
Thanks, UDS. That was very informative.
I nominate Sir Ringo.
I think William Shatner would have been a good choice, what with being The Big Giant Head and all.
UDS said it best.
For those who retain the Queen as head of state, (i.e. parliamentary systems with this) there was actually a requirement for them to determine if their particular constitutions allowed the recent change where male heirs took precedence. (Fortunately, with Charles, Willy, and George, the point will probably be irrelevant for almost 100 years).
Similarly, the Commonwealth is just an organization. The Queen as head is just a formality; it could technically be anyone. It took is a convenience, as it settles arguments - you don’t get one country saying “How come X gets to be head instead of our guy?” The Queen comes with the least political baggage as she is (allegedly) above politics. (As pointed out, it could have been Mandela if the opportunity arose, someone else head and shoulders above petty politics). So the choice of Charles is, once again, a convenience, a way to prevent inter-nation rivalries and disputes. And conveniently, the head is mainly a figurehead, so it leaves the members free to do the usual international wrangling without intervention for favouritism or partisanship from the “head”.
Wait, that Balfour Declaration? Or a different one?
Signed, a Zionist
ETA: Whatever that means nowadays.
The Australian states formed a Commonwealth in 1901. What that meant was that they didn’t want to form a Federation. That is, they wanted the Australian states to be more independent than the American states were: they wanted less Federal power.
There continues to be arguments in the United Kingdom about how much power should be federalised and how much should be devolved.
A different one. Balfour was a busy boy, declarations-wise.
Another nod to everything UDS has said, spot on.
It’s significance, as UDS alludes to, is less in terms of the responsibilities involved and more about the vote of confidence in Charles as a future statesman. If the Commonwealth members had decided ‘actually screw it, we’ll not have Charles’ that would be hugely embarrassing and diminish Charles’ authority in the UK and in the world.
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And it would also, I think, have diminished somewhat the cachet/standing of the British monarchy, independent of Charles’ personal standing.
The present Queen is monarch of 16 independent countries but, tellingly, there are 16 other independent countries of which she used to be monarch, but who have ditched her - starting with Pakistan in 1956, the most recent being Mauritius in 1992. If we include countries that ditched the monarchy before she came to the throne, there are more former Commonwealth realms than there are Commonwealth realms. And the list could grow; there are periodic republican rumblings in, e.g., Australia. And that’s not even thinking about former British possessions that, upon independence, never adopted the monarchy at all - i.e. they transitioned straight to being independent republics
In other words, the monarchy is acutely conscious that it’s not seen as a necessary or useful institution in many, even most, countries which which it has historic connections… Its role as the provider of the “Head of the Commonwealth”, purely symbolic though it may be, is a major element of it residual significance outside the UK. Quite apart from the present Queen’'s natural maternal affection for her eldest son, she would undoubtedly see a severing of the link between the Commonwealth and the monarchy as a bad thing for the long-term health of the family business.