If I trained this on a 30,000 word document could it give me a summary? Or would there be no need to train it in that case, and I could just tell it "Summarise this: <insert 30,000 word document>"?
30,000 words wouldn't be enough to train this from scratch - you'd ideally train from hundreds of millions of words at least.
30,000 words would be enough to finetune an existing model. If you did that, then the model would output text similar to the finetuning data. For example, if you finetuned it on shakespeare, then you might be able to use the model to make a new play, in shakespeare's style.
It still has the knowledge from the main training on data from across the whole internet, so would still know the word Shakespeare...
But you're right - the model finetuned on shakespeare would be good at writing a new play in the style of shakespeare, but would be bad at giving a critique of shakespeare's works.
The context window (block size) of this model is 1024 symbols. Symbols approximately map to words. So you can't ask it to summarize anything over 1024 words.
You can also use "Please suggest a section title for the following text".
Then that title can be used in the 2nd round, for example using a query of the form "The following is an extract from the Introduction section of a document about The benefits and disadvantages of nuclear power in sweden:"
I imagine you could do even better by finetuning the neural net on the document before asking for the recursive summary. Then it has all the information to work with, albeit in a compressed form.
