No, this is not possible. Furthermore, if you immigrate to Germany with a visit visa, you will not be able to switch this into any other kind of visa, nor will you be able to extend it.
You will either need a student visa ("zweckgebundenes Schengen-Visum Typ D") or, as a student applicant, you can get a special student appliction visa that lasts for nine months. During this time you can apply to universities and take German language courses. This is called "Studienbewerbervisum" or more specifically "zweckgebundenes Schengen-Visum Typ C" (Of course, you can also apply to universities from home, without coming to Germany for this purpose).
If you want to come to Germany solely with the purpose to study the language, you can apply for a special language course visa.
You can find more information about these visa forms at