That does work. Process:
1. Send yourself a text message.
2. Ask Siri, "Read me my text messages."
Siri will say, "You have a message from XXX", then Siri will pause for like 3 seconds, then Siri will read the message verbatim.
Things that do not work:
1. I could not get Siri to read a note. Siri will search for notes and display them, but will not read them.
2. I could not get Siri to read a web page aloud. Which is a bit weird, because I thought they implemented that feature for people with bad eyesight.
3. If you ask Siri a question, and Siri needs to query Wolfram Alpha, Siri will not read the result aloud. You have to look at the screen for the result. Which is unfortunate.