No, they don't. I haven't tested this in a while though.
Edit: Oh, I think you may mean a support response. Twilio helped me dig into the issue to great lengths. Ultimately, it was out of their hands. I think it's a lazy decision on AT&T's choice. Seems like a very rudimentary spam filter. You'd think they'd at least whitelist numbers customers are actively texting, especially if they don't contain keywords like "stop" or "spam."