Hi,
This is not recommended to do. It is fully up to you. But you have to be sure that the controls/web parts are not used at all.
Regarding the
CMS Desk - I would not recommend this - what if you will need to change something that is not synchronized over content staging? For example document permissions, bizform data, forum posts, blog comments...
It depends on you which modules you use and if something goes wrong, we can't be responsible for any damages made by removing the web project files.
Best regards,
Juraj Ondrus