Elizabeth's speech at Tilbury is a culmination of everything she has learned in her life. It encompasses the elements which not only made her a successful ruler, but kept her on the throne in the first place. Elizabeth has a thorough understanding that statecraft IS stagecraft and this is most most apparent at Tilbury more than any other instance in her reign.
First of all, a prince (man or woman) is not usually found on the battle field in the midst of things. It would have been too risky for a monarch to place themselves in harm's way; merely her presence must have been awe inspiring. For her to come down from the throne and walk amongst her soldiers, making a connection with the men who would fight for her and talking to them plainly would have cemented their loyalty and respect like no other tactic. She must have realized the impact that this would make not only in this moment, but also to all her critics who argued she was a weak ruler. Surely, after this moment (if it is true) it would have been significantly more difficult to argue that she was not a capable, masculine ruler.
Secondly, the act of wearing armor and especially the line "I know I have the body of a weak and frail woman, but I have the heart and stomach of a king, and a king of England too!" is staged in such a way that it reinforce the idea that she possess two bodies, that of a woman and that of a King. Elizabeth how important presentation is, that talk and reason can get you only so far; you must embody your thesis. This is evident in the elaborate dress that Elizabeth normally is featured which makes her seem etheral and otherworldly. But here in sharp contrast to the pomp  she usually adorns is also part of the production value.
IF this is a true event, it would have been beyond genius on Elizabeth's part.