There is a way to check whether an element was registered. Registered elements have their own constructors, while unregistered ones would use plain HTMLElement() for constructor (or HTMLUnknownElement() whether the name is not valid, but this is out of scope of the question):

document.registerElement('x-my-element');

document.createElement('x-my-element').constructor

//⇒ function x-my-element() { [native code] }

document.createElement('x-my-element-not-registered').constructor

//⇒ function HTMLElement() { [native code] }

That said, the checker might look like:

var isRegistered = function(name) {

  return document.createElement(name).constructor !== HTMLElement;

}

Or, with syntactic sugar:

String.prototype.isRegistered = function() { 

  return document.createElement(this).constructor !== HTMLElement; 

}

'x-my-element'.isRegistered()

//⇒ true

'xx-my-element'.isRegistered()

//⇒ false

The mostly careful version:

String.prototype.wasRegistered = function() { 

  switch(document.createElement(this).constructor) {

    case HTMLElement: return false; 

    case HTMLUnknownElement: return undefined; 

  }

  return true;

}

'x-my-element'.wasRegistered()

//⇒ true

'xx-my-element'.wasRegistered()

//⇒ false

'xx'.wasRegistered()

//⇒ undefined

There is no way to access a list of registered elements, AFAIK.

BTW, I still think that the try-catched registration (as proposed by @stephan-muller) suits your needs better.