Does messages send read receipts when open on the desktop, but when I am working in a different window?

IF you do have Read Receipts turned on, then that is delivered for every message that successfully shows up in your Messages client WHILE the Messages client is running - whether in the foreground or background. In your scenario, it would seem that Messages is running in the background and hence that receipt would get delivered. Cheers!

It's not a good idea to send Read Receipts because if it's spam the sender will know they have a valid message number for future spam. That's why read receipts were removed from email clients.

Just some food for thought.