Yes, this is certainly possible. You will need an advanced theme.
You should override the post_meta_points function to be empty. That will hide all mention of points on the main site.
Points are also displayed in the user profiles. This is slightly more complex to hide since it's displayed using a generic form function. The easiest way I think is to copy the function form_fields and change these two lines:
foreach ($form['fields'] as $field)
foreach ($form['fields'] as $key=>$field)
if (@$field['type']=='blank' || $key=='points')
You will also want to hide the Users tab in the admin section so that the users don't get displayed. You may wish to change the points in the admin to 0 as well.