Does the Mac "Do Not Disturb" function affect Skype calls? If I use Notification Center's "Do Not Disturb" toggle, will I still receive Skype phone/video calls? 

I know this toggle will temporarily disable banners/alerts, as those notifications are actually routed through Notification Center, but calls have a popup dialog of their own.

If not, how can I temporarily disable Skype calls? Do I need to log out?
Skype has a "Do Not Disturb" function.  If you click on the lower right hand corner of your avatar, you can select your status.



When you select "Do Not Disturb" you will not receive any notifications from Skype.