Dragmath does not render any maths - it just gives you different output code like LaTeX (TeX) or asciimath and you need some renderer for that code (that changes code to images or for example to MathML)
Even if you enable TeX filter from Administration menu it does not mean that moodle could automatically render your TeX notations inside double dollars as mathematical images. If you have given executable mimetex file in folder filter/tex permission to execute (there are different mimetex executable files for each operation system) moodle can usually use that file. If your server has some better distribution of LaTeX installed (TeTeX, TexLive, MikTeX, MacTeX etc) and if you have set correct paths to administration of TeX filter and get your TeX distro with ImageMagick or GhostScript functional you can use a larger variety of TeX commands - mimetex has rather limited set of commands.
If you install separately JsMath or AsciiMathML scripts / filters you don't necessarely need TeX based renderer (like Tex filter or LatexRender filter) at all because those scripts use other methods to produce your maths...
Dragmath button is not visible in administration of editor unless you edit adminlib.php and add that one row code that Marc has explained in Docs - usually if you want to use Dragmath plugin you won't need to hide it and don't need to edit adminlib.php at all. In moodle 2.0 DragMath will be a part of core files although it will be visible by default only if TeX filter is enabled.