> well, the fact is the use of a screen reader (or at least most) can be detected relatively easily by having an element in the screen reader flow that is hidden from sighted users

This isn't true, at least not enough to be useful. The majority of screen readers present web pages in a kind of virtual buffer, which users can browse with the arrow keys and other shortcuts (e.g. H to jump by heading). In this mode, the majority of screen readers don't fire focus events to let you know, "hey, your screen-reader-only element has been hit". You would be limited to:

1. users operating a screen reader which does fire focus events;

2. trying to highjack scroll events for this purpose; and

3. less technically-inclined users (read: beginners) who move through the page with Tab/Shift+Tab before they've learned the other keystrokes their screen reader offers.