No, she did not formally marry herself to England. This was more here way of feminising and politically utilising the traditional idea of the body politic, the king's closeness to and representation of the whole nation, and the social role of the monarch. It's important to note that Elizabeth did not immediately reject marriage, and in fact used the prospect of her marriage as a political tool for much of her reign (see for example her courtship with Francis, Duke of Anjou and Alençon) before it became apparent that she would not in the 1580's.

Even then, she never really ruled it out officially, it just became clear over time that it was unlikely. It should be noted that Elizabeth was in fact a rather deceptive and tricksy person. It was not uncommon for her to stoic, hide her feelings, lie, lead people on, and generally manipulative them. So she wasn't necessarily honest about her true feeling on marriage, indeed her own feelings do not appear to have been clear-cut and settled, she might well have married Robert Dudley, Earl of Leicester if it were pragmatically possible.