Sorry, no. The main-window.ico file is in the program files and no one has been able to come up with a way to register it per Profile.

I use a combination of Titlebar Tweaks extension - http://cosmicat.com/extensions/titletweak/ - "bumped" to make it compatible with the later versions of Firefox, and Nightly Tester Tools to show the Profile name first in the Titlebar in lieu of the "Browser Name". That way the Profile name appears in the minimized window in the Taskbar and the Titlebar

Try Titlebar Tweaker Plus: https://addons.mozilla.org/firefox/addon/93611/

To get different window icons you would probably need to have separate installations and change the icons in the icons directory in the Firefox installation directory (I see this icon: /usr/local/firefox36/icons/mozicon128.png).