No. *67 only works for blocking your caller ID, not texts.
However, there are ways on how to block your cell phone number while sending text messages. You can download an app (like Pinger) or go to a website to send a message without a name or phone number attached to it, or go to a website to send a message without a name or phone number attached to it.
Most carriers also allows you to send an anonymous text message to any phone number using your email account, just simply know which carrier the person you're texting and then plug that person's phone number into the carriers templates. For example AT&T,
On the other end, the person can reply to your text and you can communicate back and forth, from email to mobile device.
Unwanted phone calls or random text messages seem to come at all hours. They bug you at work, interrupt your dinner, or wake you up when you’re sound asleep. Check out some tips on how to stop unwanted phone calls and text messages at Consumer.ftc.gov.