If the model is in deployed mode and your list is a non production list then system will not allow you to edit the description but if it is a production list then it will allow you to edit the description.
On the other hand if your model is not in deployed mode i believe anybody can edit the description.
Just to add to what @Misbah stated, it is not considered best practice to have users manually update lists but rather have a view with a corresponding action to take care of this. Reason being, the model builder can safeguard the integrity of the list (codes, duplicates, etc.).
On the action piece, let me restate as it could be confusing and it depends. If your user needs to add single members to the list via the Create Action, then yes, that is ok but you should create another action which updates the code. And that list should be classified as Production Data. For transaction lists, then it is not best practice for end users to update the list directly.
Hope that clears it up, if not, please let me know.