Does well printed black text stay essentially unchanged on a highly compressed image of a page of text?

No. You can always make smash potatoes from a file.

You need to define what you mean by "stay essentially unchanged" You are using two specific words (stay unchanged) bonded by a very loose one (essentially).

Another word we need to define is "Quality at 10%". Quality is a process, that can not be represented as a percentage.

Let me link you to a really old test I did but defining 10% of the file size vs. an uncompressed file. Those are real numbers we can compare.

It is in Spanish, but I want you to see that some areas are affected more than others. A perfect black on the right image means no change in the information.

https://otake.com.mx/Apuntes/PruebasDeCompresion/3-CompresionJpg10Porciento.htm

But another point is that there is not just 1 JPG algorithm. There are at least two. One that uses smaller blocks. Some programs define it as 4:4:4 or 1x blocks.

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But, in my opinion, as you are asking on a photography site, not in a document archival site:

1. Save your original photos. The cost of 1 or 2 GB of disk space, vs the work you are investing in taking the photos, is INSIGNIFICANT.

2. When you are ready to deliver or generate a PDF, then you can play with the compression and resolution. If for some reason you need a change, you go back to your originals.