What happens when the baron kills your whole team?
It doesn't really say anything special. It just says executed, executed, executed, executed, executed - aced.
After testing it with a full team of five we have concluded that you don't get anything special from letting Baron ace you.
I'll leave the video in, but here is a quote from the creator: "I made that, and this is correct. It's an unused sound file from the game."
So, no nothing special is said by the announcer when you have an epic fail at Baron Nashor besides the enemy team laughing at you.
The below Baron video appears to be fake after further investigation
Here is a video the Baron 4 out of 5 on a entire team. As you can hear, "Terminated" is said after the last kill. Note that Corki wasn't at the Baron fight and this is the only video where I've found "Terminated" or Baron destroying an entire team.
Dragon does not get this same sound effect: