Yes! You can communicate individually with anyone registered on your school's classlist site by sending them a private message.
You can find the messages page by clicking on the message icon next to your profile picture or on the Parent Board. The message icon looks like this:
You can also search using a child's name if you can't remember their parent's name.
NB: if you have an admin account you can use the admin side of Classlist to send an Announcement to a group of parents, even if they are not in your class or year.