It does! But I don't think that anchored objects like the one you want to use flow particularly well across pages.
Note that I've deleted three lines at once to avoid a possibly undesired custom anchored object behavior:
It's an edge case, formatting-wise. There are a few possible use cases here - perhaps you want to build a file that is a template, and don't want to mess with anchored images when you fill the template with new text? Perhaps you're building a file that is going out for translation into a large number of languages? Perhaps you need the alt text for the red square read with the paragraph it's next to? It's not possible for me to guess, and each answer is going to be a different partially-unsatisfactory workaround.
Maybe you just want to go fill out a feature request for the text wrap of custom anchored objects to be respected by the paragraph in which they're anchored?
I typically anchor them elsewhere - that is, not in the paragraph that I need to wrap around it - and to insure correct placement and wrap, I include a post-DTP review stage "Use the Find/Change Dialog to Search for the Custom Anchored Object Anchor Character, and Eyeball Every Single Anchored Object in Every Language in This Twenty Language Translation Project" before delivery.