Define what you mean. As it stands the question is unanwerably vague.

Yes, there are multiple screen readers.

Screen readers do not need or particularly use a monitor; monitors are for sighted people.

Screen readers read what is displayed at and following their cursor. This means screenreader users need to learn to control a system with 2 cursors: one for entering text, and a different one for reading it.

People asking about multiple screens for blind users are basically asking which colour of monitor bezel blind people prefer. This is not a question. It's irrelevant.

Some OSes will not boot or will not display a GUI unless they detect a monitor, although there are HDMI dummies that can fix that. So, some blind users may have an old monitor connected, just so their OS will boot.