To answer this question one has to define what is a mystery school. That can be a matter of some discussion, but as far as I am concerned a mystery school is a school that fulfills the following conditions:
1. There is a founder, or authoritative leader, dead or living.
2. There is a community, physical or virtual, of autonomous individuals with a common intention: searching and being open for the mystery in life.
3. There is a doctrine, a philosophy or an ideology.
4. There is a path of initiations.
5. There are specific practices or rituals that form the methodology of the school.
Now, freemasonry doesn’t fulfill the first of these conditions, and only partially the third. We do have some ideas about reality, namely that we see the world as works under construction, and we do have a few ethical rules, but I wouldn’t call this a full fledged theory. One of the reasons for that is that freemasonry is accessible for people from all religious and political convictions and backgrounds, so in that realm we cannot have a collective vision.
So, in the most literal sense freemasonry is not a mystery school, but you certainly can experience it that way. It is up to you. The more basic question however is: do you believe that mysteries are a part of life? Or do yo believe that all life is rationally explainable? Do you believe that reality is just what we can sensorially perceive (be it sometimes only indirectly through scientific devices), or do you believe that there is a reality beyond that? Are there demons, angels, devas? How do you know?
I wish you a wonderful, mysterious day!
For those who want to know more about mystery schools, see: https://www.theedge.nu/en/more-info/mysteryschools
(I apologize for mistakes in my English. Blogs are cursory – not stuff for correction by a native speaker)