You could say that any non-register memory access "blocks" but I feel that's needlessly confusing. Normal async code doesn't "block" in any relevant sense when it accesses the heap.
As such a regular memory read is blocking, in that control will not switch while you're doing the read (ie your not doing anything else while it's copying). This is unlike issuing an async read, which is exactly a point where control can switch.
edit: As an example, consider synchronous memory copy vs asynchronous DMA-based memory copy. From the point of view of your thread, the synchronous copying blocks, while with the DMA-based copying the thread can do other stuff while the copying progresses.
So, in the context of async code, there's no difference from the application perspective between reading mmap'ed data and reading "regular" data (ie memory from the regular paged pool), as both could incur blocking IO.
If you're lucky and the mmap'ed data is in the system cache, then reading that data will not block and is fast. If you're unlucky and your process has been swapped out, then doing a regular memory read will block and is slow.
It's all fuzzy and my understanding is that what one use-case considers being blocked for too long might be fine for another. For instance, a web server trying to juggle many requests might use async/await for performance and find 0.1ms of blocking too much, vs. a local app that uses async/await for its programming model might be fine with 10ms of "blocking"!
https://tokio.rs/blog/2020-04-preemption#a-note-on-blocking discusses this in more detail.