Hello Kate,
Thank you for your question.
Yes, Google Classroom natively supports a setting to allow teachers to decide whether students can create new announcement.
In the teacher's Class setting, there is a setting under Stream and classwork > Stream, by changing the setting to Students can only comment, the New announcement button will hide from students while the Add comment button remains. Students can only post comments while are not allowed to post new stream announcements.
I hope it works for you.
Thank you.
-Jason Huang
Product Manager at xFanatical