It will pull updates for whatever branch you are on. So, if you originally checked out Moodle with something like
git clone -b MOODLE_35_STABLE firstname.lastname@example.org:moodle/moodle.git
...will fetch and merge whatever changes have been made on the 3.5 branch since you did the last clone or pull. As long as you have not made changes to core code then it will be 'fast forward' and there'll be no merge conflicts.
I assume that this is what you mean by 'minor updates'.
Note that any non-core plugins you add will not break this (but will not update the plugins). The plugins will not be under git control which you may or may not care about.