Hi Dave,
To the best of my memory Mythbusters has not tested your exact scenario. But based on two experiments they did do, I'd think nothing would happen. Especially with a reasonably recent shotgun.
In one episode they tried to duplicate a real situation where a bad guy and a cop were shooting at each other and the bullet from the bad guy's gun lodged in the cop's gun. Neither were shotguns. It took them quite a bit of doing, but they were able to duplicate it. At no time did anything happen to the cop's gun when the bullet entered the barrel from the wrong end, so to speak.
The other one they were trying to find out if sticking a finger into the barrel of a shotgun would do anything like what you see in cartoons. Again, no damage to the shot gun no matter what configuration they tried.
You might want to go on their web site and suggest they give it a shot (Oh groan - I blame it on listing to Roger Miller singing "Hot Rod Lincoln" while writing you

)