It would be possible to run miniBB with MSSQL if you
re-write all functions provided in setup_mysql.php, so they work with MSSQL and use its commands.
Try to study
Manual's Database Modules section and maybe it could give you some ideas. I think it would be pretty easy, except there could be some difficulties implementing
LIMIT X,Y statement in SELECTs (as I remember this was the main sticking point in other databases rather than mySQL - but maybe it's improved already in MSSQL itself).
We ourselves are not able to work on additional database modules for now. In the past (for miniBB 1.x) there were both postgreSQL and MSSQL modules programmed, but they paid a very weak interest. That's why we decided to concentrate on the pop technologies and discontinued what was unprofitable.
So whatever you read is possible to implement, and miniBB has all doors for it. But we have no ready modules and have no support regarding this topic.