Not necessarily, depending on your definition of 'cumbersome'.
Each OS/version of Firefox has, as you say, a default profile location; actually the locations vary more between OS versions than versions of Firefox. CCleaner already has to 'know' these locations to do what it does. In the default location, there is always a profiles.ini file which tells Firefox where to look for the profile; it is by editing this file that you point Firefox to an alternative location.
So either CCleaner could read this file (not, considering the sophistication of the program, a hard task for the Piriform team to code), or there could just be a setting to change the location; there already appears to be a Registry key that could host the relevant value.
David