Is there a plugin/way to disable uploads completely?

This isn’t very user-friendly but you could certainly change permissions on the uploads folder to prevent files from being written to them.

You can also try a role-management plug-in like Role Scoper, Role Manager, Adminimize or Capability Manager. I haven’t used any of these personally so I can’t recommend one in particular but you could experiment. Some may not be compatible with 3.3.1.

As a third option, you could probably add a function to functions.php to disable the uploads button. Something like this – but I’m not sure if this is 3.3-compatible:

https://www.ads-software.com/support/topic/hide-some-media-upload-buttonsfunctions?replies=16#post-1733215