I am going to use some sculpting to give a better shape to a Game Character, so I would like to know if Sculpting may add more geometry, for an instance the F layer brush or the F blob brush.
Normally sculpting does not add any vertices or edges, it just moves them around. But when you enable the
dynamic topology option in the left toolbar
T of your 3d view it adds vertices depending on the given value and your zoom level.
You wrote that you want to create a game character? I recommend that you copy your existing object and add more and more details. Then you can bake the normals and save a lot of memory and rendering time.