Yes, District staff can invite non District users (gmail.com or any Google account) into their Google Meet sessions. The organizer will be prompted to accept the external visitor to join the Meet.
Three ways to invite someone from outside the district
1. Sending them the link of the created meeting, they will need to ask to join the meeting and the meeting organizer need to accept them.
2. Inviting them from a Calendar event at least 15 minutes before the event takes place, and they need to join with the email address they were invited and there's no need to Ask to join.
3. Inviting them once the meeting has started from the 'Add people' section at meet.google.com, they'll receive an email with the joining details and no need to ask to join.
From inside the Google Classroom is a little different -
For meetings in Classroom, the teacher has the option to show or hide the link for students. In Classroom, the first one to join becomes the organizer so we recommend hiding the link until the time for the class comes and the teacher to be the first one to join. Only internal users can see the link in Classroom, if teachers has students that are using an external email address, he will need to send them over the invite with the link of the meeting and accept them when they request to join.