You shouldn't lose your desktop by removing ubuntu-desktop, because it is a meta-package that simply allows to easily install all default packages in the Ubuntu Desktop environment. However, it is recommended to install it again before any system upgrades.
You can safely remove gedit and ubuntu-desktop, then install ubuntu-desktop again. It will automatically select gedit for installation, because gedit is included in the meta-package.
Although is perfectly safe to do what you want, is usually unnecessary to re-install applications, unless they got corrupted by a power outage or broken update. As @sagarchalise commented, deleting the config files for the application usually solve most problems and if you are looking to reset your customizations, then that is the way to go. Re-installing won't change any personal customization.
Note: after reading your message about losing your desktop, I did a
test on a VM, just to make sure
nothing has changed since Maverick. I
didn't lose my desktop even after
rebooting and I was able to install
both packages again.