No. You get the sense she cares deeply but regrettably her job is to do nothing. Project stability. If it represents what actually happened she probably was, behind the scenes, responsible for ending the coal strike.
To me the strength of the British monarchy is that it puts ultimate authority and power in the hands of somebody who has no need for a political agenda (certainly not a party political agenda) and whose only duty is to the constitution of their country and to the welfare of that country. And they are also people who are raised to do their duty to their country and to love their country. They are only allowed to intervene in cases where the system isn't working the way it is meant to, and they can only intervene to put it back on the path it is meant to be on. While things are working the way they are supposed to be working, they must stand back and watch.
'The Crown' is quite good at showing this, especially in its first season - it's becoming more fantastic and less factually accurate as it gets closer to the present day, but it does still show that.
The royal family are not perfect people. They don't always do the right thing in every aspect of their lives. But when it comes to their core constitutional duties, I'd honestly find it hard to find a case of them failing in those duties since Edward VIII abdicated - and while doing that was a failure, at least it was a failure that meant he could do no further harm. He wasn't suitable to be King - he wasn't willing to put country above self - but at least he knew it.
Nobody would create the Westminster system of constitutional monarchy from scratch today - it would be an absurdity - but it has organically evolved over a thousand years into something that I actually do think works very well in its context. And some of the scenes in 'The Crown' do do an excellent job of showing this - most notably when the Queen calls in Winston Churchill to tell him she knows he's been keeping things from her, and making it clear this is not to happen again. We don't know how accurate that scene is - private audiences between the monarch and the Prime Minister are just that, private - but the basic message matches the reality. The Monarch intervenes only rarely, and only with cause. But the fact the Monarch can intervene, means governments normally do what they could - if the Monarch has to intervene, the system hasn't worked properly, and that is the government's responsibility.