Your question is old, so this advice might be pointless. FileMaker has grown in capacity over the years and in version 11, can have a file size of 8TB, 1 million tables per file, and 64 quadrillion total records per table. You can see many other limitations at their specification page at:
Technical specifications of FileMaker Pro 11 and FileMaker Pro 11 Advanced | FileMaker
Those things aside, huge files with thousands of users and transactions happening at the same time are still in the realm of large SQL databases like Oracle, Postgre, DB2, MS SQL Server, etc. But most needs exhibited by school database needs fit well within FileMaker. The Advanced FileMaker server used to have a limit of 1000 concurrent users, but it is now unlimited by license and limited only by your hardware and bandwidth. Keep in mind this is for FileMaker clients and web connections are limited to 100 concurrent connections.
The reason you would choose FileMaker is because it tends to be easier to develop which is useful if you don't have full time IT people to help you make your database. FileMaker in a single product that takes care of the user interface, reports, web, and database backend. And FileMaker does a pretty good job of keeping this fairly simple. Not that you can't get more complicated, but learning Access and managing MS SQL Server database is a bigger learning curve. Now if you already have full time developers who know those tools, then they might be a good way to go and you know SQL Server is very scalable.
FileMaker has the ability through ODBC to read SQL databases and that is a good way to enhance a FileMaker solution. This works well if you are primarily making FileMaker databases and only need some SQL access for your school management system data. FileMaker is not a native SQL front end tool and will not perform as fast as those tools will. If you plan to create new files and tables in FileMaker and have links to SQL Server, FileMaker is a good solution. If you plan to have all your data in SQL Server, then you will be better off with a SQL front end tool.
FileMaker is known for its ability to easily create very good looking user interfaces and reports. The tools it has lets it be a good Rapid Application Development Tool. Traditional tools on the SQL side of things get much more complicated. Personally I am not a fan of Access. If you need to write a front end with a SQL Tool, I would look at Servoy instead of Access. But that's just my 2 cents.
As previously mentioned, FileMaker supports ODBC so that FileMaker can read MS SQL Server databases as well as others like Oracle and MySQL. This also works the other way. Your School Management System SQL database can make SQL connections to your FileMaker data via the ODBC connection too if that is desirable.
One last useful tool FileMaker has is the ability with a single click to turn on secure client/server connections so that all of your data is encrypted using triple DES encryption. As security becomes more of an issue, having a one-click encryption solution sure is nice. And there are no certificates to manage or anything like that. Having encryption and combining it with authentication through Active Directory is pretty much a corporate standard now and I assume schools are having to step up security on personal information too.