A screen reader can read all the text in a post, alt text should be just a replacement for the image it is attached to. What you are missing if you can't visually see the image is what should be captured in the alt text, nothing extra.

There are cases of people making images with text that contain hashtag text (either they are screenshots or cross platform organizing images, usually) which feels like a separate set of conceptual uses for the hashtag that aren't searchable functions.