In theory, yes, in practice, probably not.
The queen doesn't really have any power now, I mean technically she does but if she ever tried to use those powers there would be chaos.
I mean the things like when the new PM goes and asks her permission to lead the country is just more for tradition than anything.
I wouldn't under estimate the Queen and her role in the UK and the world. She may not be a politician, but she knows how to play politics and has huge influence both here in the UK and around the world. She is a great ambassador for our country and probably one of the most experienced in the world. The Queen is Head of the Commonwealth which is an incredibly important alliance between nations that share common values such as: democracy, human rights, good governance, the rule of law, individual liberty, egalitarianism, free trade, multilateralism and world peace.
For more about the Queen's role in the UK see below...
When the Commissioners stand in front of that table and and read the packet of bills, they wait for The Queen to say, "Approved." Everybody is standing because it is supposed to be more or less automatic, and it's only supposed to take a few seconds.
Yet there is still no way around La Reine s'avisera! if it is ever uttered. That's it. Period. End of report.
It is a guarantee that the government cannot ever get but so out of hand.
Everybody talks as if this hasn't happened recently, but no less a leader than Tony Blair asked for The Queen to refuse to allow the second reading of an act that would have taken away his government's right to move troops around without Parliamentary approval. It was a constitutional issue because it compromised the position of The Queen as Commander in Chief, and he asked her to intervene.