Hairline cracks on artex ceiling. Will it fall in?

Hi. My suggestion is if it’s not moving it’s definitely not falling down what could solve your issue is scraping off the loose artex once it becomes more difficult to remove don’t try scraping more. Apply a layer of pvc and let dry then apply your new artex matching the patterns if you have any with a sponge or soft brush.

I would be better coming an taking a look for you an seeing it for myself

This tends to be quite normal. I would presume the cracks that appear are dead straight and either 1200 from the wall or 1200 apart. The cracks you tend to see are usually the plasterboard lines behind the artex. If, as you say there is no push on them, and, the area is not damp, I would consider this just as movement. The floor joists on which you walk upon upstairs is also the ceiling so movement is inevitable. What I do to fix this problem is use scrim tape to tape the cracks and replaster. You can also do the same with easifill and try blend in with old artex. Or just keep filling the crack, if doing this dig the crack out slightly deeper and fill.
In terms of seeing the blemish, this is called flashing. Fill area, sand area, paint area, paint whole ceiling.
The chances of a ceiling falling in are very slim, unless water is involved, its more likely to just sag.