The system requirements for moodle are pretty standard. Php5.4 and several common database servers are supported. While the free hosting page doesn't specifically state which version of php (hint) is used, the supported apps and softaculous installer lead me to believe they have at least php5.4; but I could be wrong.
The only thing I can see that might be a problem is the installation requirement for a protected data directory; I'm not sure if the free hosting allows you to edit directory access rules (.htaccess), but I'm fairly certain you can do this with cpanel. The preferred method is to install moodle under or outside the web root, but the .htaccess should work. Without a protected web directory moodle will not install.
Another consideration is the amount of web space free hosting provides. The download is around 50mb, but software like this will eat through disc space pretty quickly. 1000mb might not get you very far with something like moodle; but if you wanted it for testing/developing or just for a small site it might be appropriate.
Check moodle release docs for anything I might have missed.