GIT -- Updating a shared Host Moodle

Hi,

This is probably a rather lame question but I want to confirm what I believe to be the case.  I have been experimenting with using GIT to update my install of Moodle on my laptop, and find it very useful and efficient.  However, I manage a couple of Moodle installations that are on shared Hosted services.  My question .... In order to use GIT on those hosted installations, I assume that I have to install GIT on the server of the Hosted service and then create a Moodle repository, with the Moodle version I want to 'pull' into the 'moodle' directory.  This assumes that my Host provider will let me install GIT.  Can anyone confirm this to be the case? 

Thanks for taking time to answer.