Well, they definitely have time to edit. The http://on-camera-audiences.com/shows/midnight\'>taping schedule posted at OCA implies that there are 5 days between tape and air for each episode (Monday\'s show was taped last Wednesday).
I have personal experience: I went to the taping on Monday, and it was the Kumail Nanjiani/Natasha Leggero/Doug Benson show that aired that night. My semi-educated guess is that the episodes taped last week were essentially \"dress rehearsal\" shows which are being held to use for emergency \"evergreen\" purposes.
I\'m not sure if the comedians got anything in advance of the taping, but it did appear that they were getting some help from the show writers during the commercial breaks for the answers they were writing on their tablets.
Save for Doug Benson I haven\'t heard of a contestant yet.
You must not listen to many podcasts.