Will I be able to intergrate Joomla, Moodle and a Support Desk solution (one listed in supported programs) on one site with amember?
Yes. But all signups must come via aMember, and single-login will work only 50% (user must login to aMember then it logged to all other scripts, but it does not work between Joomla and Moodle for example).
What do you mean does not work between Joomla and Moodle? One could not go from Joomla to moodle and stay logged in?
If he logged to Joomla directly, he won't be logged to Moodle. If he logs in to aMember, he is logged-in to both Joomla and Moodle. If he logs in to Joomla, he is logged-in to aMember (but not to other scripts).