I remember my oldest son's very first IEP meeting. We were transitioning from early intervention services to Early Childhood Special Education. We got to the meeting and the OT was absent. She hadn't informed us she wasn't going to be there. My husband and I had both taken off of work for this meeting and there were quite a few team members in the room with us. We were told our only options were to excuse her or reschedule the meeting. I had been working in higher education disability services for years, but didn't know much about K-12 laws or procedures at that time so we chose to proceed without her.
I may have made the same choice today, rather than having to reschedule the entire meeting, but I have a lot more information at my disposal to make that decision today. Ask yourself, what is the value of having that person there? Do they know your child or are they only attending because they are legally obligated to be there? Are you able to talk to that person before the meeting and get their input and/or ask questions? Will that person be responsible for implementing any part of the IEP?
In your particular case, what are your thoughts on "the student is not and will not be participating in the general education environment?" Obviously, if you are seeking general education inclusion of your child in any capacity then it might be prudent for the general education teacher to be there. If you believe your child's needs will be completely supported by special education teachers and staff then the general education teacher may not be as important. However, remember that the school can send any general education teacher. In my son's case, he's in a self contained special education classroom but he still has general education teachers for classes like music, art and gym class. Often, the general ed teacher in our meetings has been one of those specials teachers that know him and can make suggestions to accommodations, services, etc. that he has needed for support.