Screen readers and other assistive technologies do not read the raw HTML or the visual page directly; they query the accessibility tree that the browser constructs, which is why correct semantic HTML and ARIA matter so much: they directly shape what ends up in that tree. Elements hidden with display:none or aria-hidden are excluded from the tree entirely, while purely decorative elements marked correctly are also excluded so they do not clutter the experience.
Browser developer tools (in Chrome, Firefox, and Safari) all include an accessibility tree inspector, which is one of the most reliable ways to see exactly what a screen reader user will encounter.