This is a good idea to add resources to the project via "Add existing file" and to add application icon from a separate file. Main thing here is the convenience for maintenance and no risk to screw up something not related to the separate icon or bitmap file.
For icons, I would advice using the freeware editor IcoFX:
http://en.wikipedia.org/wiki/IcoFX[
^],
http://icofx.ro/[
^].
Of course it supports transparency, but also a lot more, in particular, good quality re-sampling for different icon sizes; and you can manually improve the results. (As you probably know, and icon should contain several images for a set of standard icon sizes; if you fail to do it, it will still be shown correctly, but re-sampling will be done be during the run time of your application, with questionable quality.)
You can also edit the main image or part of it using some editor of your choice, and then finally edit or package it using IcoFX. I suggest you try two open-source products: GIMP (pixel graphics) and Inkscape (vector, based on SVG, import/export from/to many formats, including (importantly!) XAML):
http://en.wikipedia.org/wiki/GIMP[
^],
http://www.gimp.org/[
^];
http://en.wikipedia.org/wiki/Inkscape[
^],
http://inkscape.org/[
^].
Good luck,
—SA