I do not know what solution can be detected automatically if the user uses a screen reader. but there is a google solution to hide the link at the top of the page (left: -1000em and position: absolute), which can be activated if you use the keyboard and display "special mode".
<a href="#" style="left:-1000em;position:absolute">Screen reader users, click here to turn off Google Instant.</a>
for your modal dialog, try using the aria attribute and aria-atomic = "true" aria-live = "assertive" in the html div dialog box. it should declare the contents of your dialog box.
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