The editor (TeXMaker) is irrelevant to the question.
In MiKTeX settings, if you chose "Install missing packages on the fly", it means that MiKTeX will do automatic installation for any file requested during compilation that is in its file name database.
More clearly, if you're running (pdf|xe|lua)(la)tex etc., and the engine tries to load a file that is not on the computer, MiKTeX will check the file name database online. If it finds the file, it interrupts the compilation and downloads the package containing that file.
If you type
kpsewhich --help in the command prompt, it will give you a list of all the file types it handles. (I don't know if automatic package installation works for all of them.)
So yes, packages, classes and fonts etc. can be installed on the fly.
There is also a handy trick that you can use. If you want to install a specific package without opening the Package Manager, you can usually do
.pdf for the documentation and it will automatically download the package.